메뉴 건너뛰기




Volumn 1917, Issue , 2008, Pages 1-156

Existence and Regularity Properties of the Integrated Density of States of Random Schrödinger Operators

(1)  Veselić, Ivan a  

a NONE

Author keywords

[No Author keywords available]

Indexed keywords


EID: 37149033775     PISSN: 00758434     EISSN: None     Source Type: Book Series    
DOI: None     Document Type: Review
Times cited : (54)

References (501)
  • 1
    • 0008293098 scopus 로고
    • A note on the Følner condition for amenability
    • T. Adachi. A note on the Følner condition for amenability. Nagoya Math. J., 131:67-74, 1993.
    • (1993) Nagoya Math. J , vol.131 , pp. 67-74
    • Adachi, T.1
  • 2
    • 51249162086 scopus 로고
    • Density of states in spectral geometry
    • T. Adachi and T. Sunada. Density of states in spectral geometry. Comment. Math. Helv., 68(3):480-493, 1993.
    • (1993) Comment. Math. Helv , vol.68 , Issue.3 , pp. 480-493
    • Adachi, T.1    Sunada, T.2
  • 4
    • 0001324593 scopus 로고
    • Localization at weak disorder: Some elementary bounds
    • 65A
    • M. Aizenman. Localization at weak disorder: some elementary bounds. Rev. Math. Phys., 6(5A): 1163-1182, 1994.
    • (1994) Rev. Math. Phys , pp. 1163-1182
    • Aizenman, M.1
  • 6
    • 30544454224 scopus 로고    scopus 로고
    • Moment analysis for localization in random Schrödinger operators
    • M. Aizenman, A. Elgart, S. Naboko, J. H. Schenker, and G. Stolz. Moment analysis for localization in random Schrödinger operators. Invent. Math., 163(2):343-413, 2006. http://www.ma.utexas.edu/mp.arc/03-377.
    • (2006) Invent. Math , vol.163 , Issue.2 , pp. 343-413
    • Aizenman, M.1    Elgart, A.2    Naboko, S.3    Schenker, J.H.4    Stolz, G.5
  • 7
    • 0032516668 scopus 로고    scopus 로고
    • Localization bounds for an electron gas
    • M. Aizenman and G. M. Graf. Localization bounds for an electron gas. J. Phys. A, 31(32):6783-6806, 1998. http://www.ma.utexas.edu/mp.arc/97- 540.
    • (1998) J. Phys. A , vol.31 , Issue.32 , pp. 6783-6806
    • Aizenman, M.1    Graf, G.M.2
  • 8
    • 0001607449 scopus 로고
    • Uniqueness of the infinite cluster and continuity of connectivity functions for short and long range percolation
    • M. Aizenman, H. Kesten, and C. M. Newman. Uniqueness of the infinite cluster and continuity of connectivity functions for short and long range percolation. Comm. Math. Phys., 111(4):505-531, 1987.
    • (1987) Comm. Math. Phys , vol.111 , Issue.4 , pp. 505-531
    • Aizenman, M.1    Kesten, H.2    Newman, C.M.3
  • 9
    • 21344491724 scopus 로고
    • Localization at large disorder and at extreme energies: An elementary derivation
    • M. Aizenman and S. Molchanov. Localization at large disorder and at extreme energies: an elementary derivation. Comm. Math. Phys., 157(2):245-278, 1993.
    • (1993) Comm. Math. Phys , vol.157 , Issue.2 , pp. 245-278
    • Aizenman, M.1    Molchanov, S.2
  • 10
    • 0033727833 scopus 로고    scopus 로고
    • Constructive fractional-moment criteria for localization in random operators
    • M. Aizenman, J. H. Schenker, R. M. Friedrich, and D. Hundertmark. Constructive fractional-moment criteria for localization in random operators. Phys. A, 279(1-4):369-377, 2000.
    • (2000) Phys. A , vol.279 , Issue.1-4 , pp. 369-377
    • Aizenman, M.1    Schenker, J.H.2    Friedrich, R.M.3    Hundertmark, D.4
  • 11
    • 0035643446 scopus 로고    scopus 로고
    • Finite-volume fractional-moment criteria for Anderson localization
    • M. Aizenman, J. H. Schenker, R., M. Friedrich, and D. Hundertmark. Finite-volume fractional-moment criteria for Anderson localization. Comm. Math. Phys., 224(1):219-253, 2001.
    • (2001) Comm. Math. Phys , vol.224 , Issue.1 , pp. 219-253
    • Aizenman, M.1    Schenker, J.H.2    Friedrich, R.M.3    Hundertmark, D.4
  • 12
    • 84990553776 scopus 로고
    • Brownian motion and Harnack inequality for Schrödinger operators
    • M. Aizenman and B. Simon. Brownian motion and Harnack inequality for Schrödinger operators. Commun. Pure Appl. Math., 35:209-273, 1982.
    • (1982) Commun. Pure Appl. Math , vol.35 , pp. 209-273
    • Aizenman, M.1    Simon, B.2
  • 13
    • 33645979029 scopus 로고    scopus 로고
    • Absolutely continuous spectra of quantum tree graphs with weak disorder
    • doi: 10.1007/s00220-005-1468-5
    • M. Aizenman, R. Sims, and S. Waxzel. Absolutely continuous spectra of quantum tree graphs with weak disorder. Comm. Math. Phys., 264:371, 2006. doi: 10.1007/s00220-005-1468-5.
    • Comm. Math. Phys , vol.264 , Issue.371 , pp. 2006
    • Aizenman, M.1    Sims, R.2    Waxzel, S.3
  • 14
    • 57049139335 scopus 로고    scopus 로고
    • Fluctuation-based proof of the stability of ac spectra of random operators on tree graphs
    • Amer. Math. Soc, Providence, RI
    • M. Aizenman, R. Sims, and S. Warzel. Fluctuation-based proof of the stability of ac spectra of random operators on tree graphs. In Quantum graphs and their applications, volume 415 of Contemp. Math., pages 1-14. Amer. Math. Soc., Providence, RI, 2006.
    • (2006) Quantum graphs and their applications, volume 415 of Contemp. Math , pp. 1-14
    • Aizenman, M.1    Sims, R.2    Warzel, S.3
  • 16
    • 33747884265 scopus 로고    scopus 로고
    • R.and Warzel. Stability of the absolutely continuous spectrum of random Schrödinger operators on tree graphs
    • M. Aizenman and S. Sims, R.and Warzel. Stability of the absolutely continuous spectrum of random Schrödinger operators on tree graphs. Probab. Theory Related Fields, 136(3):363-394, 2006.
    • (2006) Probab. Theory Related Fields , vol.136 , Issue.3 , pp. 363-394
    • Aizenman, M.1    Sims, S.2
  • 17
    • 84941395042 scopus 로고
    • Ergodic theorems for superadditive processes
    • M. A. Akcoglu and U. Krengel. Ergodic theorems for superadditive processes. J. Reine Angew. Math., 323:53-67, 1981.
    • (1981) J. Reine Angew. Math , vol.323 , pp. 53-67
    • Akcoglu, M.A.1    Krengel, U.2
  • 18
    • 0003487664 scopus 로고
    • Theory of linear operators in Hubert space
    • 9 of, Pitman, Boston, Mass
    • N. I. Akhiezer and I. M. Glazman. Theory of linear operators in Hubert space. Vol. I, volume 9 of Monographs and Studies in Mathematics. Pitman, Boston, Mass., 1981.
    • (1981) Monographs and Studies in Mathematics , vol.1
    • Akhiezer, N.I.1    Glazman, I.M.2
  • 19
    • 0003487664 scopus 로고
    • Theory of linear operators in Hilbert space
    • 10 of, Pitman, Boston, Mass
    • N. I. Akhiezer and I. M. Glazman. Theory of linear operators in Hilbert space. Vol. II, volume 10 of Monographs and Studies in Mathematics. Pitman, Boston, Mass., 1981.
    • (1981) Monographs and Studies in Mathematics , vol.2
    • Akhiezer, N.I.1    Glazman, I.M.2
  • 20
    • 24244444170 scopus 로고
    • Absence of diffusion in certain random lattices
    • P. Anderson. Absence of diffusion in certain random lattices. Phys. Rev., 109:1492, 1958.
    • (1958) Phys. Rev , vol.109 , pp. 1492
    • Anderson, P.1
  • 21
    • 33644905267 scopus 로고    scopus 로고
    • The spectrum of Schrödinger operators with Poisson type random potential
    • K. Ando, A. Iwatsuka, M. Kaminaga, and F. Nakano. The spectrum of Schrödinger operators with Poisson type random potential. Ann. Henri Poincaré, 7(1):145-160, 2006.
    • (2006) Ann. Henri Poincaré , vol.7 , Issue.1 , pp. 145-160
    • Ando, K.1    Iwatsuka, A.2    Kaminaga, M.3    Nakano, F.4
  • 22
    • 0001225381 scopus 로고
    • Spectre du laplacien et écrasement d'anses
    • C. Anne. Spectre du laplacien et écrasement d'anses. Ann. Sci. École Norm. Sup. (4), 20(2):271-280, 1987.
    • (1987) Ann. Sci. École Norm. Sup. (4) , vol.20 , Issue.2 , pp. 271-280
    • Anne, C.1
  • 23
    • 0000139890 scopus 로고
    • Enlargement of obstacles for the simple random walk
    • P. Antal. Enlargement of obstacles for the simple random walk. Ann. Probab., 23(3):1061-1101, 1995.
    • (1995) Ann. Probab , vol.23 , Issue.3 , pp. 1061-1101
    • Antal, P.1
  • 25
    • 85009425644 scopus 로고    scopus 로고
    • T. Antunović and I. Veselić. Spectral asymptotics of percolation Hamiltoninas on amenable Cayley graphs. Accepted for publication in the proceedings of OTAMP 2006 in the series Operator Theory: Advances and Applications.
    • T. Antunović and I. Veselić. Spectral asymptotics of percolation Hamiltoninas on amenable Cayley graphs. Accepted for publication in the proceedings of OTAMP 2006 in the series Operator Theory: Advances and Applications.
  • 27
    • 0001259850 scopus 로고
    • On a problem of Weyl in the theory of singular Sturm-Liouville equations
    • N. Aronszajn. On a problem of Weyl in the theory of singular Sturm-Liouville equations. Amer. J. Math., 79:597-610, 1957.
    • (1957) Amer. J. Math , vol.79 , pp. 597-610
    • Aronszajn, N.1
  • 28
    • 52449142230 scopus 로고
    • On exponential representations of analytic functions in the upper half-plane with positive imaginary part
    • N. Aronszajn and W. F. Donoghue. On exponential representations of analytic functions in the upper half-plane with positive imaginary part. J. Analyse Math., 5:321-388, 1957.
    • (1957) J. Analyse Math , vol.5 , pp. 321-388
    • Aronszajn, N.1    Donoghue, W.F.2
  • 29
    • 51249195797 scopus 로고
    • A supplement to the paper on exponential representations of analytic functions in the upper half-plane with positive imaginary part
    • N. Aronszajn and W. F. Donoghue. A supplement to the paper on exponential representations of analytic functions in the upper half-plane with positive imaginary part. J. Analyse Math., 12:113-127, 1964.
    • (1964) J. Analyse Math , vol.12 , pp. 113-127
    • Aronszajn, N.1    Donoghue, W.F.2
  • 30
    • 0002951048 scopus 로고
    • Elliptic operators, discrete groups and von Neumann algebras
    • Astérisque, Soc. Math. France, Paris
    • M. F. Atiyah. Elliptic operators, discrete groups and von Neumann algebras. In Colloque "Analyse et Topologie" en l'Honneur de Henri Cartan (Orsay, 1974), pages 43-72. Astérisque, No. 32-33. Soc. Math. France, Paris, 1976.
    • (1976) Colloque "Analyse et Topologie" en l'Honneur de Henri Cartan (Orsay, 1974) , Issue.32-33 , pp. 43-72
    • Atiyah, M.F.1
  • 31
    • 33749356721 scopus 로고    scopus 로고
    • Reducibility or nonuniform hyperbolicity for quasiperiodic Schrödinger cocycles
    • A. Avila and R. Krikorian. Reducibility or nonuniform hyperbolicity for quasiperiodic Schrödinger cocycles. Ann. of Math. (2), 164(3):911-940, 2006.
    • (2006) Ann. of Math. (2) , vol.164 , Issue.3 , pp. 911-940
    • Avila, A.1    Krikorian, R.2
  • 32
    • 84972566320 scopus 로고
    • Almost periodic Schrödinger operators. II. The integrated density of states
    • J. Avron and B. Simon. Almost periodic Schrödinger operators. II. The integrated density of states. Duke Math. J., 50(1):369-391, 1983.
    • (1983) Duke Math. J , vol.50 , Issue.1 , pp. 369-391
    • Avron, J.1    Simon, B.2
  • 33
    • 0007130625 scopus 로고    scopus 로고
    • Landau Hamiltonians with unbounded random potentials
    • J.-M. Barbaroux, J.-M. Combes, and P. D. Hislop. Landau Hamiltonians with unbounded random potentials. Lett. Math. Phys., 40(4):355-369, 1997.
    • (1997) Lett. Math. Phys , vol.40 , Issue.4 , pp. 355-369
    • Barbaroux, J.-M.1    Combes, J.-M.2    Hislop, P.D.3
  • 34
    • 0002271908 scopus 로고    scopus 로고
    • Localization near band edges for random Schrödinger operators
    • J.-M. Barbaroux, J.-M. Combes, and P. D. Hislop. Localization near band edges for random Schrödinger operators. Helv. Phys. Acta, 70(1-2):16-43, 1997.
    • (1997) Helv. Phys. Acta , vol.70 , Issue.1-2 , pp. 16-43
    • Barbaroux, J.-M.1    Combes, J.-M.2    Hislop, P.D.3
  • 36
    • 84953818707 scopus 로고
    • A norm inequality for a "finite-section" Wiener-Hopf equation
    • G. Baxter. A norm inequality for a "finite-section" Wiener-Hopf equation. Illinois J. Math., 7:97-103, 1963.
    • (1963) Illinois J. Math , vol.7 , pp. 97-103
    • Baxter, G.1
  • 37
    • 85009411176 scopus 로고    scopus 로고
    • J. Bellissard. Gap labelling theorems for Schrödinger operators. In M. Waldschmidt, P. Moussa, J. M. Luck, and C. Itzykson., editors, From number theory to physics (Les Houches, 1989), pages 538-630, Berlin, 1992. Springer. Number Theory and Physics, meeting at Les Houches (France), March 7-16, 1989.
    • J. Bellissard. Gap labelling theorems for Schrödinger operators. In M. Waldschmidt, P. Moussa, J. M. Luck, and C. Itzykson., editors, From number theory to physics (Les Houches, 1989), pages 538-630, Berlin, 1992. Springer. Number Theory and Physics, meeting at Les Houches (France), March 7-16, 1989.
  • 38
    • 29444445483 scopus 로고    scopus 로고
    • Spaces of tilings, finite telescopic approximations and gap-labeling
    • J. Bellissard, R. Benedetti, and J.-M. Gambaudo. Spaces of tilings, finite telescopic approximations and gap-labeling. Comm. Math. Phys., 261(1):1-41, 2006.
    • (2006) Comm. Math. Phys , vol.261 , Issue.1 , pp. 1-41
    • Bellissard, J.1    Benedetti, R.2    Gambaudo, J.-M.3
  • 40
    • 0037568994 scopus 로고
    • Almost periodic Schrödinger operators
    • World Sci. Publishing, Singapore
    • J. Bellissard, R. Lima, and D. Testard. Almost periodic Schrödinger operators. In Mathematics + physics. Vol. 1, pages 1-64. World Sci. Publishing, Singapore, 1985.
    • (1985) Mathematics + physics , vol.1 , pp. 1-64
    • Bellissard, J.1    Lima, R.2    Testard, D.3
  • 41
    • 21844487920 scopus 로고
    • The noncommutative geometry of the quantum Hall effect
    • J. Bellissard, A. van Eist, and H. Schulz-Baldes. The noncommutative geometry of the quantum Hall effect. J. Math. Phys., 35(10):5373-5451, 1994.
    • (1994) J. Math. Phys , vol.35 , Issue.10 , pp. 5373-5451
    • Bellissard, J.1    van Eist, A.2    Schulz-Baldes, H.3
  • 42
    • 85009345685 scopus 로고    scopus 로고
    • M.-T. Benameur and H. Oyono-Oyono. Gap-labelling for quasi-crystals (proving a conjecture by J. Bellissard). In Operator algebras and mathematical physics (Constanţa, 2001), pages 11-22. Theta, Bucharest, 2003.
    • M.-T. Benameur and H. Oyono-Oyono. Gap-labelling for quasi-crystals (proving a conjecture by J. Bellissard). In Operator algebras and mathematical physics (Constanţa, 2001), pages 11-22. Theta, Bucharest, 2003.
  • 43
    • 84956264307 scopus 로고
    • On the spectrum of the one-dimensional Schrödinger equation with a random potential
    • M. Benderskii and L. Pastur. On the spectrum of the one-dimensional Schrödinger equation with a random potential. Math. USSR, Sb., 11:245, 1970.
    • (1970) Math. USSR, Sb , vol.11 , pp. 245
    • Benderskii, M.1    Pastur, L.2
  • 44
    • 0000102289 scopus 로고
    • Espaces de Dirichlet. I. Le cas élémentaire
    • A. Beurling and J. Deny. Espaces de Dirichlet. I. Le cas élémentaire. Acta Math., 99:203-224, 1958.
    • (1958) Acta Math , vol.99 , pp. 203-224
    • Beurling, A.1    Deny, J.2
  • 46
    • 85009378400 scopus 로고    scopus 로고
    • M. Š. Birman and M. Z. Solomjak. Estimates for the singular numbers of integral operators. Uspehi Mat. Nauk, 32(1(193)):17-84, 271, 1977. [English transl.:Russ. Math. Surv. 32(1): 15-89, 1977].
    • M. Š. Birman and M. Z. Solomjak. Estimates for the singular numbers of integral operators. Uspehi Mat. Nauk, 32(1(193)):17-84, 271, 1977. [English transl.:Russ. Math. Surv. 32(1): 15-89, 1977].
  • 47
    • 0003647398 scopus 로고
    • Spectral theory of selfadjoint operators in Hilbert space
    • Mathematics and its Applications , D. Reidel Publishing Co, Dordrecht
    • M. Š. Birman and M. Z. Solomjak. Spectral theory of selfadjoint operators in Hilbert space. Mathematics and its Applications (Soviet Series). D. Reidel Publishing Co., Dordrecht, 1987.
    • (1987) Soviet Series
    • Birman, M.S.1    Solomjak, M.Z.2
  • 48
    • 0003647398 scopus 로고
    • Spectral theory of self-adjoint operators in Hilbert space
    • Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, Russian original: Leningrad. Univ, Leningrad
    • M. S. Birman and M. Solomyak. Spectral theory of self-adjoint operators in Hilbert space. Mathematics and Its Applications. Soviet Series. 5. Kluwer Academic Publishers, Dordrecht, 1987. [Russian original: Leningrad. Univ., Leningrad, 1980].
    • (1980) Soviet Series , vol.5
    • Birman, M.S.1    Solomyak, M.2
  • 49
    • 0001890867 scopus 로고    scopus 로고
    • A periodic magnetic Hamiltonian with a variable metric. The problem of absolute continuity
    • M. Š. Birman and T. A. Suslina. A periodic magnetic Hamiltonian with a variable metric. The problem of absolute continuity. Algebra i Analiz, 11(2):1-40, 1999.
    • (1999) Algebra i Analiz , vol.11 , Issue.2 , pp. 1-40
    • Birman, M.S.1    Suslina, T.A.2
  • 50
    • 0000614853 scopus 로고
    • The spectral shift function. The work of M.G. Krein and its further development
    • M. Š. Birman and D. Yafaev. The spectral shift function. The work of M.G. Krein and its further development. St. Petersburg Math. J., 4:833-870, 1993.
    • (1993) St. Petersburg Math. J , vol.4 , pp. 833-870
    • Birman, M.S.1    Yafaev, D.2
  • 52
    • 0035537280 scopus 로고    scopus 로고
    • Long-time tails in the parabolic Anderson model with bounded potential
    • M. Biskup and W. König. Long-time tails in the parabolic Anderson model with bounded potential. Ann. Probab., 29(2):636-682, 2001.
    • (2001) Ann. Probab , vol.29 , Issue.2 , pp. 636-682
    • Biskup, M.1    König, W.2
  • 57
    • 23844514826 scopus 로고    scopus 로고
    • Linear response theory for magnetic Schrödinger operators in disordered media
    • J.-M. Bouclet, F. Germinet, A. Klein, and J. H. Schenker. Linear response theory for magnetic Schrödinger operators in disordered media. J. Funct. Anal., 226(2):301-372, 2005. http://www.arxiv.org/math-ph/0408028.
    • (2005) J. Funct. Anal , vol.226 , Issue.2 , pp. 301-372
    • Bouclet, J.-M.1    Germinet, F.2    Klein, A.3    Schenker, J.H.4
  • 58
    • 0036016733 scopus 로고    scopus 로고
    • Absolutely continuous spectrum for ID quasiperiodic operators
    • J. Bourgain and S. Jitomirskaya. Absolutely continuous spectrum for ID quasiperiodic operators. Invent. Math., 148(3):453-463, 2002.
    • (2002) Invent. Math , vol.148 , Issue.3 , pp. 453-463
    • Bourgain, J.1    Jitomirskaya, S.2
  • 59
    • 22344450797 scopus 로고    scopus 로고
    • On localization in the continuous Anderson-Bernoulli model in higher dimension
    • J. Bourgain and C. E. Kenig. On localization in the continuous Anderson-Bernoulli model in higher dimension. Invent. Math., 161(2):389-426, 2005.
    • (2005) Invent. Math , vol.161 , Issue.2 , pp. 389-426
    • Bourgain, J.1    Kenig, C.E.2
  • 60
    • 34247469755 scopus 로고    scopus 로고
    • Localization near fluctuation boundaries via, fractional moments and applications
    • A. Boutet de Monvel, S. Naboko, P. Stollmann, and G. Stolz. Localization near fluctuation boundaries via, fractional moments and applications. J. Anal. Math., 100:83-116, 2006.
    • (2006) J. Anal. Math , vol.100 , pp. 83-116
    • Boutet de Monvel, A.1    Naboko, S.2    Stollmann, P.3    Stolz, G.4
  • 61
    • 0037251665 scopus 로고    scopus 로고
    • Dynamical localization for continuum random surface models
    • A. Boutet de Monvel and P. Stollmann. Dynamical localization for continuum random surface models. Arch. Math. (Basel), 80(1):87-97, 2003.
    • (2003) Arch. Math. (Basel) , vol.80 , Issue.1 , pp. 87-97
    • Boutet de Monvel, A.1    Stollmann, P.2
  • 63
    • 33744543086 scopus 로고    scopus 로고
    • The integrated density of states in strong magnetic fields
    • P. Briet and G. Raikov. The integrated density of states in strong magnetic fields. J. Funct. Anal., 237(2):540-564, 2006.
    • (2006) J. Funct. Anal , vol.237 , Issue.2 , pp. 540-564
    • Briet, P.1    Raikov, G.2
  • 65
    • 0034395580 scopus 로고    scopus 로고
    • Continuity properties of Schrödinger semigroups with magnetic fields
    • K. Broderix, D. Hundertmark, and H. Leschke. Continuity properties of Schrödinger semigroups with magnetic fields. Rev. Math. Phys., 12(2): 181-225, 2000.
    • (2000) Rev. Math. Phys , vol.12 , Issue.2 , pp. 181-225
    • Broderix, K.1    Hundertmark, D.2    Leschke, H.3
  • 66
    • 3142749044 scopus 로고    scopus 로고
    • Continuous integral kernels for unbounded Schrödinger semigroups and their spectral projections
    • K. Broderix, H. Leschke, and P. Müller. Continuous integral kernels for unbounded Schrödinger semigroups and their spectral projections. J. Funct. Anal., 212(2):287-323, 2004. http://www.arXiv.org/math-ph/0209020.
    • (2004) J. Funct. Anal , vol.212 , Issue.2 , pp. 287-323
    • Broderix, K.1    Leschke, H.2    Müller, P.3
  • 67
    • 2442690978 scopus 로고    scopus 로고
    • Spectral shift function in strong magnetic fields
    • V. Bruneau, A. Pushnitski, and G. Raikov. Spectral shift function in strong magnetic fields. Algebra i Analiz, 16(1):207-238, 2004.
    • (2004) Algebra i Analiz , vol.16 , Issue.1 , pp. 207-238
    • Bruneau, V.1    Pushnitski, A.2    Raikov, G.3
  • 68
    • 5744228040 scopus 로고    scopus 로고
    • High energy asymptotics of the magnetic spectral shift function
    • V. Bruneau and G. D. Raikov. High energy asymptotics of the magnetic spectral shift function. J. Math. Phys., 45(9):3453-3461, 2004.
    • (2004) J. Math. Phys , vol.45 , Issue.9 , pp. 3453-3461
    • Bruneau, V.1    Raikov, G.D.2
  • 69
    • 85009378395 scopus 로고    scopus 로고
    • J. Brüning and T. Sunada. On the spectrum of gauge-periodic elliptic operators. Astérisque, (210):6, 65-74, 1992. Méthodes semi-classiques, 2 (Nantes, 1991).
    • J. Brüning and T. Sunada. On the spectrum of gauge-periodic elliptic operators. Astérisque, (210):6, 65-74, 1992. Méthodes semi-classiques, Vol. 2 (Nantes, 1991).
  • 70
    • 84972500756 scopus 로고
    • On the spectrum of periodic elliptic operators
    • J. Brüning and T. Sunada. On the spectrum of periodic elliptic operators. Nagoya Math. J., 126:159-171, 1992.
    • (1992) Nagoya Math. J , vol.126 , pp. 159-171
    • Brüning, J.1    Sunada, T.2
  • 73
    • 33646889414 scopus 로고    scopus 로고
    • A proof of the Ishii-Pastur theorem by the method of subordinacy
    • D. Buschmann. A proof of the Ishii-Pastur theorem by the method of subordinacy. Univ. Iagel Acta Math., (34):29-34, 1997.
    • (1997) Univ. Iagel Acta Math , vol.34 , pp. 29-34
    • Buschmann, D.1
  • 74
    • 23044523773 scopus 로고    scopus 로고
    • D. Buschmann and G. Stolz. Two-parameter spectral averaging and localization for non-monotonic random Schrödinger operators. Trans. Amer. Math. Soc., 353(2):635-653 (electronic), 2001. Preprint No.: 98-617 http://www.ma.utexas.edu/mp.arc/.
    • D. Buschmann and G. Stolz. Two-parameter spectral averaging and localization for non-monotonic random Schrödinger operators. Trans. Amer. Math. Soc., 353(2):635-653 (electronic), 2001. Preprint No.: 98-617 http://www.ma.utexas.edu/mp.arc/.
  • 78
    • 84972583190 scopus 로고
    • Exponential localization in one dimensional disordered systems
    • R. Carmona,. Exponential localization in one dimensional disordered systems. Duke Math. J., 49:191-213, 1982.
    • (1982) Duke Math. J , vol.49 , pp. 191-213
    • Carmona, R.1
  • 79
    • 0001518561 scopus 로고
    • One-dimensional Schrödinger operators with random or deterministic potentials: New spectral types
    • R. Carmona. One-dimensional Schrödinger operators with random or deterministic potentials: New spectral types. J. Functional Anal., 51:229-258, 1983.
    • (1983) J. Functional Anal , vol.51 , pp. 229-258
    • Carmona, R.1
  • 80
    • 0002362803 scopus 로고
    • Anderson localization for Bernoulli and other singular potentials
    • R. Carmona, A. Klein, and F. Martinelli. Anderson localization for Bernoulli and other singular potentials. Commun. Math. Phys., 108:41-66, 1987.
    • (1987) Commun. Math. Phys , vol.108 , pp. 41-66
    • Carmona, R.1    Klein, A.2    Martinelli, F.3
  • 82
    • 0006990260 scopus 로고    scopus 로고
    • Densité intégrée d'états surfaciques et fonction généralisée de déplacement spectral pour un opérateur de Schrödinger surfacique ergodique
    • A. Chahrour. Densité intégrée d'états surfaciques et fonction généralisée de déplacement spectral pour un opérateur de Schrödinger surfacique ergodique. Helv. Phys. Acta, 72(2):93-122, 1999.
    • (1999) Helv. Phys. Acta , vol.72 , Issue.2 , pp. 93-122
    • Chahrour, A.1
  • 83
    • 0006984318 scopus 로고    scopus 로고
    • On the spectrum of the Schrödinger operator with periodic surface potential
    • A. Chahrour. On the spectrum of the Schrödinger operator with periodic surface potential. Lett. Math. Phys., 52(3):197-209, 2000.
    • (2000) Lett. Math. Phys , vol.52 , Issue.3 , pp. 197-209
    • Chahrour, A.1
  • 85
    • 51249185116 scopus 로고
    • Spectra of manifolds with small handles
    • I. Chavel and E. A. Feldman. Spectra of manifolds with small handles. Comment. Math. Helv., 56(1):83-102, 1981.
    • (1981) Comment. Math. Helv , vol.56 , Issue.1 , pp. 83-102
    • Chavel, I.1    Feldman, E.A.2
  • 86
    • 15244349841 scopus 로고
    • On the density of states for the quantum percolation problem
    • J. T. Chayes, L. Chayes, J. R. Franz, J. P. Sethna, and S. A. Trugman. On the density of states for the quantum percolation problem. J. Phys. A, 19(18) :L1173-L1177, 1986.
    • (1986) J. Phys. A , vol.19 , Issue.18
    • Chayes, J.T.1    Chayes, L.2    Franz, J.R.3    Sethna, J.P.4    Trugman, S.A.5
  • 87
    • 0040531556 scopus 로고    scopus 로고
    • 2-invariants
    • 2-invariants. Michigan Math. J., 46(2):331-346, 1999.
    • (1999) Michigan Math. J , vol.46 , Issue.2 , pp. 331-346
    • Clair, B.1
  • 88
    • 33847654434 scopus 로고
    • Asymptotic behaviour of eigenfunctions for multiparticle Schrödinger operators
    • J. Combes and L. Thomas. Asymptotic behaviour of eigenfunctions for multiparticle Schrödinger operators. Commun. Math. Phys., 34:251-270, 1973.
    • (1973) Commun. Math. Phys , vol.34 , pp. 251-270
    • Combes, J.1    Thomas, L.2
  • 89
    • 0001026869 scopus 로고
    • Localization for some continuous, random Hamiltionians in d-dimensions
    • J.-M. Combes and P. Hislop. Localization for some continuous, random Hamiltionians in d-dimensions. J. Funct. Anal., 124:149-180, 1994.
    • (1994) J. Funct. Anal , vol.124 , pp. 149-180
    • Combes, J.-M.1    Hislop, P.2
  • 93
    • 0037275377 scopus 로고    scopus 로고
    • Holder continuity of the integrated density of states for some random operators at all energies
    • J.-M. Combes, P. D. Hislop, and F. Klopp. Holder continuity of the integrated density of states for some random operators at all energies. Int. Math. Res. Not., (4): 179-209, 2003.
    • (2003) Int. Math. Res. Not , vol.4 , pp. 179-209
    • Combes, J.-M.1    Hislop, P.D.2    Klopp, F.3
  • 94
    • 0036475771 scopus 로고    scopus 로고
    • The Wegner estimate and the integrated density of states for some random operators
    • J.-M. Combes, P. D. Hislop, F. Klopp, and S. Nakamura. The Wegner estimate and the integrated density of states for some random operators. Proc. Indian Acad. Sci. Math. Sci., 112(1):31-53, 2002. www.ias.ac.in/mathsci/.
    • (2002) Proc. Indian Acad. Sci. Math. Sci , vol.112 , Issue.1 , pp. 31-53
    • Combes, J.-M.1    Hislop, P.D.2    Klopp, F.3    Nakamura, S.4
  • 95
    • 8744313700 scopus 로고    scopus 로고
    • Global continuity of the integrated density of states for random Landau Hamiltonians
    • preprint 03-272 on
    • J.-M. Combes, P. D. Hislop, F. Klopp, and G. Raikov. Global continuity of the integrated density of states for random Landau Hamiltonians. Commun. Part. Diff Eqns., 29:1187-1214, 2004. preprint 03-272 on www.ma.utexas.edu/mpjirc/, 2003.
    • (2003) Commun. Part. Diff Eqns , vol.29 , pp. 1187-1214
    • Combes, J.-M.1    Hislop, P.D.2    Klopp, F.3    Raikov, G.4
  • 97
    • 0035531720 scopus 로고    scopus 로고
    • p-theory of the spectral shift function, the Wegner estimate, and the integrated density of states for some random Schrödinger operators
    • p-theory of the spectral shift function, the Wegner estimate, and the integrated density of states for some random Schrödinger operators. Commun. Math. Phys., 70(218):113-130, 2001.
    • (2001) Commun. Math. Phys , vol.70 , Issue.218 , pp. 113-130
    • Combes, J.-M.1    Hislop, P.D.2    Nakamura, S.3
  • 98
    • 0000951121 scopus 로고    scopus 로고
    • Band edge localization and the density of states for acoustic and electromagnetic waves in random media
    • J.-M. Combes, P. D. Hislop, and A. Tip. Band edge localization and the density of states for acoustic and electromagnetic waves in random media. Ann. Inst. H. Poincaré Phys. Théor., 70(4):381-428, 1999.
    • (1999) Ann. Inst. H. Poincaré Phys. Théor , vol.70 , Issue.4 , pp. 381-428
    • Combes, J.-M.1    Hislop, P.D.2    Tip, A.3
  • 99
    • 0001449373 scopus 로고
    • Log Hölder continuity of the integrated density of states for stochastic Jacobi matrices
    • W. Craig and B. Simon. Log Hölder continuity of the integrated density of states for stochastic Jacobi matrices. Commun. Math. Phys., 90:207-218, 1983.
    • (1983) Commun. Math. Phys , vol.90 , pp. 207-218
    • Craig, W.1    Simon, B.2
  • 100
    • 84972546484 scopus 로고
    • Subharmonicity of the Lyaponov index
    • W. Craig and B. Simon. Subharmonicity of the Lyaponov index. Duke Math. J., 50:551-560, 1983.
    • (1983) Duke Math. J , vol.50 , pp. 551-560
    • Craig, W.1    Simon, B.2
  • 101
    • 0001891854 scopus 로고
    • Weak type estimates for singular values and the number of bound states of Schrödinger operators
    • M. Cwikel. Weak type estimates for singular values and the number of bound states of Schrödinger operators. Ann. Math. (2), 106(1):93-100, 1977.
    • (1977) Ann. Math. (2) , vol.106 , Issue.1 , pp. 93-100
    • Cwikel, M.1
  • 102
    • 0043048970 scopus 로고
    • Schrödinger Operators with Application to Quantum Mechanics and Global Geometry
    • Springer, Berlin
    • H. L. Cycon, R. G. Froese, W. Kirsch, and B. Simon. Schrödinger Operators with Application to Quantum Mechanics and Global Geometry. Text and Monographs in Physics. Springer, Berlin, 1987.
    • (1987) Text and Monographs in Physics
    • Cycon, H.L.1    Froese, R.G.2    Kirsch, W.3    Simon, B.4
  • 103
    • 0037905892 scopus 로고    scopus 로고
    • Analytic torsion and R.-torsion for manifolds with boundary
    • X. Dai and H. Fang. Analytic torsion and R.-torsion for manifolds with boundary. Asian J. Math., 4(3):695-714, 2000.
    • (2000) Asian J. Math , vol.4 , Issue.3 , pp. 695-714
    • Dai, X.1    Fang, H.2
  • 104
    • 0037099097 scopus 로고    scopus 로고
    • D. Damanik, R. Sims, and G. Stolz. Localization for one-dimensional, continuum, Bernoulli-Anderson models. Duke Math. J., 114(1):59-100, 2002. preprint No.: 00-404, www.ma.utexas.edu/mp.arc/.
    • D. Damanik, R. Sims, and G. Stolz. Localization for one-dimensional, continuum, Bernoulli-Anderson models. Duke Math. J., 114(1):59-100, 2002. preprint No.: 00-404, www.ma.utexas.edu/mp.arc/.
  • 106
    • 1542511261 scopus 로고    scopus 로고
    • Localization for discrete one-dimensional random word models
    • D. Damanik, R. Sims, and G. Stolz. Localization for discrete one-dimensional random word models. J. Funct. Anal., 208(2):423-445, 2004.
    • (2004) J. Funct. Anal , vol.208 , Issue.2 , pp. 423-445
    • Damanik, D.1    Sims, R.2    Stolz, G.3
  • 107
    • 0035634523 scopus 로고    scopus 로고
    • Multi-scale analysis implies strong dynamical localization
    • D. Damanik and P. Stollmann. Multi-scale analysis implies strong dynamical localization. Geom. Funct. Anal., 11(1):11-29, 2001. http://www.ma.utexas.edu/mp_arc/c/99/99-461.ps.gz.
    • (2001) Geom. Funct. Anal , vol.11 , Issue.1 , pp. 11-29
    • Damanik, D.1    Stollmann, P.2
  • 109
    • 0003035519 scopus 로고
    • Spectral properties of compact manifolds and changes of metric
    • E. B. Davies. Spectral properties of compact manifolds and changes of metric. Amer. J. Math., 112(1):15-39, 1990.
    • (1990) Amer. J. Math , vol.112 , Issue.1 , pp. 15-39
    • Davies, E.B.1
  • 110
    • 0000787440 scopus 로고
    • The functional calculus
    • E. B. Davies. The functional calculus. J. London Math. Soc., 52:166-176, 1995.
    • (1995) J. London Math. Soc , vol.52 , pp. 166-176
    • Davies, E.B.1
  • 111
    • 0034339654 scopus 로고    scopus 로고
    • Dynamical localization for the random dimer Schrödinger operator
    • S. De Bièvre and F. Germinet. Dynamical localization for the random dimer Schrödinger operator. J. Statist. Phys., 98(5-6):1135-1148, 2000.
    • (2000) J. Statist. Phys , vol.98 , Issue.5-6 , pp. 1135-1148
    • De Bièvre, S.1    Germinet, F.2
  • 112
    • 0039881855 scopus 로고
    • Amas accidentels dans les solutions solides désordonnées
    • P.-G. de Gennes, P. Lafore, and J. Millot. Amas accidentels dans les solutions solides désordonnées. J. of Phys. and Chem. of Solids, 11(1-2):105-110, 1959.
    • (1959) J. of Phys. and Chem. of Solids , vol.11 , Issue.1-2 , pp. 105-110
    • de Gennes, P.-G.1    Lafore, P.2    Millot, J.3
  • 113
    • 0041024712 scopus 로고
    • Sur un phénomène de propagation dans un milieu désordonné
    • P.-G. de Gennes, P. Lafore, and J. Mihot. Sur un phénomène de propagation dans un milieu désordonné. J. Phys. Rad., 20:624, 1959.
    • (1959) J. Phys. Rad , vol.20 , pp. 624
    • de Gennes, P.-G.1    Lafore, P.2    Mihot, J.3
  • 114
    • 0001091673 scopus 로고
    • Almost periodic Schrödinger operators. III. The absolutely continuous spectrum in one dimension
    • P. Deift and B. Simon. Almost periodic Schrödinger operators. III. The absolutely continuous spectrum in one dimension. Comm. Math. Phys., 90(3):389-411, 1983.
    • (1983) Comm. Math. Phys , vol.90 , Issue.3 , pp. 389-411
    • Deift, P.1    Simon, B.2
  • 115
    • 0001346875 scopus 로고
    • Anderson localization for multidimensional systems at large disorder or large energy
    • F. Delyon, Y. Levy, and B. Souillard. Anderson localization for multidimensional systems at large disorder or large energy. Comm. Math. Phys., 100(4) :463-470, 1985.
    • (1985) Comm. Math. Phys , vol.100 , Issue.4 , pp. 463-470
    • Delyon, F.1    Levy, Y.2    Souillard, B.3
  • 116
    • 0000010934 scopus 로고
    • Remark on the continuity of the density of states of ergodic finite-difference operators
    • F. Delyon and B. Souillard. Remark on the continuity of the density of states of ergodic finite-difference operators. Commun. Math. Phys., 94:289-291, 1984.
    • (1984) Commun. Math. Phys , vol.94 , pp. 289-291
    • Delyon, F.1    Souillard, B.2
  • 118
    • 0001133825 scopus 로고
    • 2-cohomology of infinite coverings
    • 2-cohomology of infinite coverings. Topology, 16(2):157-165, 1977.
    • (1977) Topology , vol.16 , Issue.2 , pp. 157-165
    • Dodziuk, J.1
  • 119
    • 0001921997 scopus 로고
    • Maximum principle for parabolic inequalities and the heat flow on open manifolds
    • J. Dodziuk. Maximum principle for parabolic inequalities and the heat flow on open manifolds. Indiana University Mathematics Journal, 32(5):704-716, 1983.
    • (1983) Indiana University Mathematics Journal , vol.32 , Issue.5 , pp. 704-716
    • Dodziuk, J.1
  • 120
    • 85009345680 scopus 로고    scopus 로고
    • 2 -Spectral Invariants and the Integrated Density of States
    • J. Dodziuk, N. Lenz, D. Peyerimhoff, T. Schick, and I. Veselić, editors, of
    • 2 -Spectral Invariants and the Integrated Density of States, volume 3 of Oberwolfach Rep., 2006. http://www.mfo.de/ programme/schedule/2006/08b/OWR.2006.09.pdf.
    • (2006) Oberwolfach Rep , vol.3
  • 123
    • 0001281413 scopus 로고    scopus 로고
    • 2 invariants of amenable covering spaces: A combinatorial approach
    • 2 invariants of amenable covering spaces: a combinatorial approach. J. Funct. Anal., 154(2):359-378, 1998.
    • (1998) J. Funct. Anal , vol.154 , Issue.2 , pp. 359-378
    • Dodziuk, J.1    Mathai, V.2
  • 124
    • 85009407983 scopus 로고    scopus 로고
    • 2 torsion on amenable covering spaces. math.DG/0008211 on arxiv.org, see also [121].
    • 2 torsion on amenable covering spaces. math.DG/0008211 on arxiv.org, see also [121].
  • 125
    • 0035534688 scopus 로고    scopus 로고
    • The uniqueness of the integrated density of states for the Schrödinger operators with magnetic fields
    • S.-I. Doi, A. Iwatsuka, and T. Mine. The uniqueness of the integrated density of states for the Schrödinger operators with magnetic fields. Math. Z., 237(2): 335-371, 2001.
    • (2001) Math. Z , vol.237 , Issue.2 , pp. 335-371
    • Doi, S.-I.1    Iwatsuka, A.2    Mine, T.3
  • 126
    • 0002202859 scopus 로고
    • 2-Betti numbers for abelian groups
    • 2-Betti numbers for abelian groups. Canad. Math. Bull., 24(1):91-95, 1981.
    • (1981) Canad. Math. Bull , vol.24 , Issue.1 , pp. 91-95
    • Donnelly, H.1
  • 127
    • 84981761432 scopus 로고
    • On the perturbation of spectra
    • W. F. Donoghue, Jr. On the perturbation of spectra. Comm. Pure Appl. Math., 18:559-579, 1965.
    • (1965) Comm. Pure Appl. Math , vol.18 , pp. 559-579
    • Donoghue Jr., W.F.1
  • 129
    • 84980196462 scopus 로고
    • On the number of distinct sites visited by a random walk
    • M. D. Donsker and S. R. S. Varadhan. On the number of distinct sites visited by a random walk. Comm. Pure Appl Math., 32(6):721-747, 1979.
    • (1979) Comm. Pure Appl Math , vol.32 , Issue.6 , pp. 721-747
    • Donsker, M.D.1    Varadhan, S.R.S.2
  • 130
    • 0000515551 scopus 로고
    • Localisation in a single-band approximation to random Schrödinger operators in a magnetic field
    • T. C. Dorias, N. Maoris, and J. V. Pule. Localisation in a single-band approximation to random Schrödinger operators in a magnetic field. Helv. Phys. Acta, 68(4):329-364, 1995.
    • (1995) Helv. Phys. Acta , vol.68 , Issue.4 , pp. 329-364
    • Dorias, T.C.1    Maoris, N.2    Pule, J.V.3
  • 131
    • 0030532040 scopus 로고    scopus 로고
    • Localization in single Landau bands
    • T. C. Dorlas, N. Macris, and J. V. Pule. Localization in single Landau bands. J. Math. Phys., 37(4):1574-1595, 1996.
    • (1996) J. Math. Phys , vol.37 , Issue.4 , pp. 1574-1595
    • Dorlas, T.C.1    Macris, N.2    Pule, J.V.3
  • 132
    • 0031138777 scopus 로고    scopus 로고
    • The nature of the spectrum for a Landau Hamiltonian with delta impurities
    • T. C. Dorlas, N. Macris, and J. V. Pule. The nature of the spectrum for a Landau Hamiltonian with delta impurities. J. Statist. Phys., 87(3-4):847-875, 1997.
    • (1997) J. Statist. Phys , vol.87 , Issue.3-4 , pp. 847-875
    • Dorlas, T.C.1    Macris, N.2    Pule, J.V.3
  • 133
    • 0033241786 scopus 로고    scopus 로고
    • Characterization of the spectrum of the Landau Hamiltonian with delta impurities
    • T. C. Dorlas, N. Macris, and J. V. Pulé. Characterization of the spectrum of the Landau Hamiltonian with delta impurities. Comm. Math. Phys., 204(2):367-396, 1999.
    • (1999) Comm. Math. Phys , vol.204 , Issue.2 , pp. 367-396
    • Dorlas, T.C.1    Macris, N.2    Pulé, J.V.3
  • 134
    • 0000528504 scopus 로고
    • On the C*-algebra of Toeplitz operators on the quarter-plane
    • R. G. Douglas and R. Howe. On the C*-algebra of Toeplitz operators on the quarter-plane. Trans. Amer. Math. Soc., 158:203-217, 1971.
    • (1971) Trans. Amer. Math. Soc , vol.158 , pp. 203-217
    • Douglas, R.G.1    Howe, R.2
  • 136
    • 34249966896 scopus 로고
    • A new proof of localization in the Anderson tight binding model
    • H. v. Dreifus and A. Klein. A new proof of localization in the Anderson tight binding model. Comm. Math. Phys., 124(2):285-299, 1989.
    • (1989) Comm. Math. Phys , vol.124 , Issue.2 , pp. 285-299
    • Dreifus, H.V.1    Klein, A.2
  • 137
    • 38249041049 scopus 로고
    • The effect of boundary conditions on the density of states for random Schrödinger operators
    • J. Droese and W. Kirsch. The effect of boundary conditions on the density of states for random Schrödinger operators. Stochastic Process. Appl., 23(1):169-175, 1986.
    • (1986) Stochastic Process. Appl , vol.23 , Issue.1 , pp. 169-175
    • Droese, J.1    Kirsch, W.2
  • 138
    • 0002570054 scopus 로고
    • Curvature-induced bound states in quantum waveguides in two and three dimensions
    • P. Duclos and P. Exner. Curvature-induced bound states in quantum waveguides in two and three dimensions. Rev. Math. Phys., 7(1):73-102, 1995.
    • (1995) Rev. Math. Phys , vol.7 , Issue.1 , pp. 73-102
    • Duclos, P.1    Exner, P.2
  • 139
    • 0035648814 scopus 로고    scopus 로고
    • Bound states in curved quantum layers
    • P. Duelos, P. Exner, and D. Krejčiřík. Bound states in curved quantum layers. Comm. Math. Phys., 223(1):13-28, 2001.
    • (2001) Comm. Math. Phys , vol.223 , Issue.1 , pp. 13-28
    • Duelos, P.1    Exner, P.2    Krejčiřík, D.3
  • 144
    • 85009344879 scopus 로고    scopus 로고
    • D. V. Efremov and M. A. Shubin. Spectrum distribution function and variational principle for automorphic operators on hyperbolic space. In Séminaire sur les Équations aux Dérivées Partielles, 1988-1989, pages Exp. No. VIII, 19. Ecole Polytech., Palaiseau, 1989.
    • D. V. Efremov and M. A. Shubin. Spectrum distribution function and variational principle for automorphic operators on hyperbolic space. In Séminaire sur les Équations aux Dérivées Partielles, 1988-1989, pages Exp. No. VIII, 19. Ecole Polytech., Palaiseau, 1989.
  • 146
    • 0036025748 scopus 로고    scopus 로고
    • Equality of bulk and edge Hall conductance revisited
    • P. Elbau and G. M. Graf. Equality of bulk and edge Hall conductance revisited. Comm. Math. Phys., 229(3):415-432, 2002.
    • (2002) Comm. Math. Phys , vol.229 , Issue.3 , pp. 415-432
    • Elbau, P.1    Graf, G.M.2
  • 148
    • 85009411186 scopus 로고    scopus 로고
    • 2-spectral invariants and quasi-crystal graphs. http://www.arXiv.org/abs/math/0607198.
    • 2-spectral invariants and quasi-crystal graphs. http://www.arXiv.org/abs/math/0607198.
  • 149
    • 0001401431 scopus 로고
    • Floquet solutions for the 1-dimensional quasi-periodic Schrödinger equation
    • L. H. Eliasson. Floquet solutions for the 1-dimensional quasi-periodic Schrödinger equation. Comm. Math. Phys., 146(3):447-482, 1992.
    • (1992) Comm. Math. Phys , vol.146 , Issue.3 , pp. 447-482
    • Eliasson, L.H.1
  • 150
    • 0003264261 scopus 로고
    • Stochastic differential equations on manifolds
    • of, Cambridge University Press, Cambridge
    • K. D. Elworthy. Stochastic differential equations on manifolds, volume 70 of London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge, 1982.
    • (1982) London Mathematical Society Lecture Note Series , vol.70
    • Elworthy, K.D.1
  • 151
    • 19544390510 scopus 로고
    • Group structure and the pointwise ergodic theorem for connected amenable groups
    • W. Emerson and F. P. Greenleaf. Group structure and the pointwise ergodic theorem for connected amenable groups. Advances in Mathematics, 14:153-172, 1974.
    • (1974) Advances in Mathematics , vol.14 , pp. 153-172
    • Emerson, W.1    Greenleaf, F.P.2
  • 152
    • 0011575455 scopus 로고
    • Covering properties and Følner conditions for locally compact groups
    • W. R. Emerson and F. P. Greenleaf. Covering properties and Følner conditions for locally compact groups. Math. Z., 102:370-384, 1967.
    • (1967) Math. Z , vol.102 , pp. 370-384
    • Emerson, W.R.1    Greenleaf, F.P.2
  • 155
    • 0032346360 scopus 로고    scopus 로고
    • Lifschitz tail in a magnetic field: The nonclassical regime
    • L. Erdos. Lifschitz tail in a magnetic field: the nonclassical regime. Probab. Theory Related Fields, 112(3):321-371, 1998.
    • (1998) Probab. Theory Related Fields , vol.112 , Issue.3 , pp. 321-371
    • Erdos, L.1
  • 156
    • 0035643283 scopus 로고    scopus 로고
    • Lifschitz tail in a magnetic field: Coexistence of classical and quantum behavior in the borderline case
    • L. Erdos. Lifschitz tail in a magnetic field: coexistence of classical and quantum behavior in the borderline case. Probab. Theory Related Fields, 121(2):219-236, 2001.
    • (2001) Probab. Theory Related Fields , vol.121 , Issue.2 , pp. 219-236
    • Erdos, L.1
  • 157
    • 0001122314 scopus 로고
    • Bound states in curved quantum waveguides
    • P. Exner and P. Seba. Bound states in curved quantum waveguides. J. Math. Phys., 30(11):2574-2580, 1989.
    • (1989) J. Math. Phys , vol.30 , Issue.11 , pp. 2574-2580
    • Exner, P.1    Seba, P.2
  • 158
    • 0000282987 scopus 로고
    • Maximum properties and inequalities for the eigenvalues of completely continuous operators
    • K. Fan. Maximum properties and inequalities for the eigenvalues of completely continuous operators. Proc Nat. Acad. Sci., U. S. A., 37:760-766, 1951.
    • (1951) Proc Nat. Acad. Sci., U. S. A , vol.37 , pp. 760-766
    • Fan, K.1
  • 159
    • 0032393327 scopus 로고    scopus 로고
    • 2 invariants
    • 2 invariants. Math. Ann., 311(2):335-375, 1998.
    • (1998) Math. Ann , vol.311 , Issue.2 , pp. 335-375
    • Farber, M.1
  • 160
    • 0030494809 scopus 로고    scopus 로고
    • Homological algebra of Novikov-Shubin invariants and Morse inequalities
    • M. S. Farber. Homological algebra of Novikov-Shubin invariants and Morse inequalities. Geom. Funct. Anal., 6(4):628-665, 1996.
    • (1996) Geom. Funct. Anal , vol.6 , Issue.4 , pp. 628-665
    • Farber, M.S.1
  • 161
    • 0036014159 scopus 로고    scopus 로고
    • Anderson transitions for a family of almost periodic Schrödinger equations in the adiabatic case
    • A. Fedotov and F. Klopp. Anderson transitions for a family of almost periodic Schrödinger equations in the adiabatic case. Comm. Math. Phys., 227(1):1-92, 2002.
    • (2002) Comm. Math. Phys , vol.227 , Issue.1 , pp. 1-92
    • Fedotov, A.1    Klopp, F.2
  • 162
    • 22044444791 scopus 로고    scopus 로고
    • The spectral theory of adiabatic quasi-periodic operators on the real line
    • A. Fedotov and F. Klopp. The spectral theory of adiabatic quasi-periodic operators on the real line. Markov Process. Related Fields, 9(4):579-614, 2003.
    • (2003) Markov Process. Related Fields , vol.9 , Issue.4 , pp. 579-614
    • Fedotov, A.1    Klopp, F.2
  • 163
    • 27844585359 scopus 로고    scopus 로고
    • A. Fedotov and F. Klopp. On the absolutely continuous spectrum of one-dimensional quasi-periodic Schrödinger operators in the adiabatic limit. Trans. Amer. Math. Soc., 357(11):4481-4516 (electronic), 2005. http://www.ma.utexas.edu/mp_arc/c/01/01-224.ps.gz.
    • A. Fedotov and F. Klopp. On the absolutely continuous spectrum of one-dimensional quasi-periodic Schrödinger operators in the adiabatic limit. Trans. Amer. Math. Soc., 357(11):4481-4516 (electronic), 2005. http://www.ma.utexas.edu/mp_arc/c/01/01-224.ps.gz.
  • 164
    • 2442696308 scopus 로고    scopus 로고
    • On the singularities of the magnetic spectral shift function at the Landau levels
    • C. Fernández and G. Raikov. On the singularities of the magnetic spectral shift function at the Landau levels. Ann. Henri Poincaré, 5(2):381-403, 2004.
    • (2004) Ann. Henri Poincaré , vol.5 , Issue.2 , pp. 381-403
    • Fernández, C.1    Raikov, G.2
  • 165
    • 0030485972 scopus 로고    scopus 로고
    • Localization of classical waves. I. Acoustic waves
    • A. Figotin and A. Klein. Localization of classical waves. I. Acoustic waves. Comm. Math. Phys., 180(2):439-482, 1996.
    • (1996) Comm. Math. Phys , vol.180 , Issue.2 , pp. 439-482
    • Figotin, A.1    Klein, A.2
  • 166
    • 0031534447 scopus 로고    scopus 로고
    • Localization of classical waves. II. Electromagnetic waves
    • A. Figotin and A. Klein. Localization of classical waves. II. Electromagnetic waves. Comm. Math. Phys., 184(2):411-441, 1997.
    • (1997) Comm. Math. Phys , vol.184 , Issue.2 , pp. 411-441
    • Figotin, A.1    Klein, A.2
  • 168
    • 0039054598 scopus 로고    scopus 로고
    • Existence of the density of states for multi-dimensional continuum Schrödinger operators with Gaussian random potentials
    • W. Fischer, T. Hupfer, H. Leschke, and P. Müller. Existence of the density of states for multi-dimensional continuum Schrödinger operators with Gaussian random potentials. Comm. Math. Phys., 190(1):133-141, 1997.
    • (1997) Comm. Math. Phys , vol.190 , Issue.1 , pp. 133-141
    • Fischer, W.1    Hupfer, T.2    Leschke, H.3    Müller, P.4
  • 169
    • 0040530133 scopus 로고    scopus 로고
    • Towards localisation by Gaussian random potentials in multi-dimensional continuous space
    • W. Fischer, H. Leschke, and P. Müller. Towards localisation by Gaussian random potentials in multi-dimensional continuous space. Lett. Math. Phys., 38(4):343-348, 1996.
    • (1996) Lett. Math. Phys , vol.38 , Issue.4 , pp. 343-348
    • Fischer, W.1    Leschke, H.2    Müller, P.3
  • 170
    • 0034549703 scopus 로고    scopus 로고
    • Spectral localization by Gaussian random potentials in multi-dimensional continuous space
    • W. Fischer, H. Leschke, and P. Müller. Spectral localization by Gaussian random potentials in multi-dimensional continuous space. J. Statist. Phys., 101(5-6):935-985, 2000.
    • (2000) J. Statist. Phys , vol.101 , Issue.5-6 , pp. 935-985
    • Fischer, W.1    Leschke, H.2    Müller, P.3
  • 171
    • 28444495091 scopus 로고    scopus 로고
    • Absolutely continuous spectrum of a class of random nonergodic Schrödinger operators
    • R. L. Frank and O. Safronov. Absolutely continuous spectrum of a class of random nonergodic Schrödinger operators. Int. Math. Res. Not., (42):2559-2577, 2005.
    • (2005) Int. Math. Res. Not , vol.42 , pp. 2559-2577
    • Frank, R.L.1    Safronov, O.2
  • 173
    • 0035535737 scopus 로고    scopus 로고
    • Realizing holonomic constraints in classical and quantum mechanics
    • R. Froese and I. Herbst. Realizing holonomic constraints in classical and quantum mechanics. Comm. Math. Phys., 220(3):489-535, 2001.
    • (2001) Comm. Math. Phys , vol.220 , Issue.3 , pp. 489-535
    • Froese, R.1    Herbst, I.2
  • 174
    • 0034394014 scopus 로고    scopus 로고
    • On the extended nature of edge states of quantum Hall Hamiltonians
    • J. Fröhlich, G. M. Graf, and J. Welcher. On the extended nature of edge states of quantum Hall Hamiltonians. Ann. Henri Poincaré, 1(3):405-442, 2000.
    • (2000) Ann. Henri Poincaré , vol.1 , Issue.3 , pp. 405-442
    • Fröhlich, J.1    Graf, G.M.2    Welcher, J.3
  • 175
    • 0002119217 scopus 로고
    • Constructive proof of localization in the Anderson tight binding model
    • J. Fröhlich, F. Martinelli, E. Scoppola, and T. Spencer. Constructive proof of localization in the Anderson tight binding model. Comm. Math. Phys., 101(1):21-46, 1985.
    • (1985) Comm. Math. Phys , vol.101 , Issue.1 , pp. 21-46
    • Fröhlich, J.1    Martinelli, F.2    Scoppola, E.3    Spencer, T.4
  • 176
    • 0000284780 scopus 로고
    • Absence of diffusion in the Anderson tight binding model for large disorder or low energy
    • J. Fröhlich and T. Spencer. Absence of diffusion in the Anderson tight binding model for large disorder or low energy. Commun. Math. Phys., 88:151-184, 1983.
    • (1983) Commun. Math. Phys , vol.88 , pp. 151-184
    • Fröhlich, J.1    Spencer, T.2
  • 177
    • 0040460272 scopus 로고
    • Collapsing of Riemannian manifolds and eigenvalues of Laplace operator
    • K. Fukaya. Collapsing of Riemannian manifolds and eigenvalues of Laplace operator. Invent. Math., 87(3):517-547, 1987.
    • (1987) Invent. Math , vol.87 , Issue.3 , pp. 517-547
    • Fukaya, K.1
  • 178
    • 84972580799 scopus 로고
    • On the spectral distribution of a disordered system and the range of a random walk
    • M. Fukushima. On the spectral distribution of a disordered system and the range of a random walk. Osaka Jour. Math., 11:73-85, 1974.
    • (1974) Osaka Jour. Math , vol.11 , pp. 73-85
    • Fukushima, M.1
  • 180
    • 0041191081 scopus 로고
    • On the asymptotic properties of spectra of a random difference operator
    • M. Fukushima, M. Nagai, and S. Nakao. On the asymptotic properties of spectra of a random difference operator. Proc Japan Acad., 51:100-102, 1975.
    • (1975) Proc Japan Acad , vol.51 , pp. 100-102
    • Fukushima, M.1    Nagai, M.2    Nakao, S.3
  • 181
    • 0040119725 scopus 로고
    • On the uniqueness of the infinite cluster in the percolation model
    • A. Gandolfi, G. Grimmett, and L. Russo. On the uniqueness of the infinite cluster in the percolation model. Comm. Math. Phys., 114(4):549-552, 1988.
    • (1988) Comm. Math. Phys , vol.114 , Issue.4 , pp. 549-552
    • Gandolfi, A.1    Grimmett, G.2    Russo, L.3
  • 182
    • 0039814783 scopus 로고
    • Concavity properties of Kreïn's spectral shift function
    • R. Geisler, V. Kostrykin, and R. Schrader. Concavity properties of Kreïn's spectral shift function. Rev. Math. Phys., 7(2):161-181, 1995.
    • (1995) Rev. Math. Phys , vol.7 , Issue.2 , pp. 161-181
    • Geisler, R.1    Kostrykin, V.2    Schrader, R.3
  • 183
    • 0040163789 scopus 로고    scopus 로고
    • Dynamical localization for discrete and continuous random Schrödinger operators
    • F. Germinet and S. De Bièvre. Dynamical localization for discrete and continuous random Schrödinger operators. Comm. Math. Phys., 194(2):323-341, 1998.
    • (1998) Comm. Math. Phys , vol.194 , Issue.2 , pp. 323-341
    • Germinet, F.1    De Bièvre, S.2
  • 184
    • 27644548596 scopus 로고    scopus 로고
    • On localization for the Schrödinger operator with a Poisson random potential
    • F. Germinet, P. Hislop, and A. Klein. On localization for the Schrödinger operator with a Poisson random potential. C. R. Math. Acad. Sci. Paris, 341(8): 525-528, 2005.
    • (2005) C. R. Math. Acad. Sci. Paris , vol.341 , Issue.8 , pp. 525-528
    • Germinet, F.1    Hislop, P.2    Klein, A.3
  • 185
    • 34250322678 scopus 로고    scopus 로고
    • Localization for Schrödinger operators with Poisson random potential
    • F. Germinet, P. Hislop, and A. Klein. Localization for Schrödinger operators with Poisson random potential. J. Europ. Math. Soc., 9(3):577-607, 2007.
    • (2007) J. Europ. Math. Soc , vol.9 , Issue.3 , pp. 577-607
    • Germinet, F.1    Hislop, P.2    Klein, A.3
  • 186
    • 0035538238 scopus 로고    scopus 로고
    • Bootstrap multiscale analysis and localization in random media
    • F. Germinet and A. Klein. Bootstrap multiscale analysis and localization in random media. Comm. Math. Phys., 222(2):415-448, 2001. http://www.-ma.utexas.edu/mp_arc/c/01/01-228.ps.gz.
    • (2001) Comm. Math. Phys , vol.222 , Issue.2 , pp. 415-448
    • Germinet, F.1    Klein, A.2
  • 187
    • 1142264344 scopus 로고    scopus 로고
    • Explicit finite volume criteria for localization in continuous random media and applications
    • F. Germinet and A. Klein. Explicit finite volume criteria for localization in continuous random media and applications. Geom. Funct. Anal., 13(6): 1201-1238, 2003. http://www.ma.utexas.edu/mp_arc/c/02/02-375. ps.gz.
    • (2003) Geom. Funct. Anal , vol.13 , Issue.6 , pp. 1201-1238
    • Germinet, F.1    Klein, A.2
  • 188
    • 4644249975 scopus 로고    scopus 로고
    • High disorder localization for random Schrödinger operators through explicit finite volume criteria
    • F. Germinet and A. Klein. High disorder localization for random Schrödinger operators through explicit finite volume criteria. Markov Process. Related Fields, 9(4):633-650, 2003. http://www.ma.utexas.edu/ mp_arc/c/02/02-425.ps.gz.
    • (2003) Markov Process. Related Fields , vol.9 , Issue.4 , pp. 633-650
    • Germinet, F.1    Klein, A.2
  • 189
    • 0037374309 scopus 로고    scopus 로고
    • Operator kernel estimates for functions of generalized Schrödinger operators
    • 911-920 electronic
    • F. Germinet and A. Klein. Operator kernel estimates for functions of generalized Schrödinger operators. Proc. Amer. Math. Soc., 131(3):911-920 (electronic), 2003. http://www.ma.utexas.edu/mp.arc/c/01/01-289. ps.gz.
    • (2003) Proc. Amer. Math. Soc , vol.131 , Issue.3
    • Germinet, F.1    Klein, A.2
  • 190
    • 4644231405 scopus 로고    scopus 로고
    • A characterization of the Anderson metal-insulator transport transition
    • F. Germinet and A. Klein. A characterization of the Anderson metal-insulator transport transition. Duke Math. J., 124(2):309-350, 2004. http://www.ma.utexas.edu/mp_arc/c/01/01-486.pdf.
    • (2004) Duke Math. J , vol.124 , Issue.2 , pp. 309-350
    • Germinet, F.1    Klein, A.2
  • 191
    • 33644530394 scopus 로고    scopus 로고
    • New characterizations of the region of complete localization for random Schrödinger operators
    • F. Germinet and A. Klein. New characterizations of the region of complete localization for random Schrödinger operators. J. Stat. Phys., 122(1):73-94, 2006.
    • (2006) J. Stat. Phys , vol.122 , Issue.1 , pp. 73-94
    • Germinet, F.1    Klein, A.2
  • 192
    • 37149009430 scopus 로고    scopus 로고
    • Dynamical delocalization in random landau hamiltonians
    • F. Germinet, A. Klein, and J. H. Schenker. Dynamical delocalization in random landau hamiltonians. Ann. of Math., 166:215-244, 2007. http://arxiv.org/abs/math-ph/0412070.
    • (2007) Ann. of Math , vol.166 , pp. 215-244
    • Germinet, F.1    Klein, A.2    Schenker, J.H.3
  • 193
    • 85009411184 scopus 로고    scopus 로고
    • F. Gesztesy, K. A. Makarov, and A. K. Motovilov. Monotonicity and concavity properties of the spectral shift function. In Stochastic processes, physics and geometry: new interplays, II (Leipzig, 1999), 29 of CMS Conf. Proc., pages 207-222. Amer. Math. Soc., Providence, RI, 2000.
    • F. Gesztesy, K. A. Makarov, and A. K. Motovilov. Monotonicity and concavity properties of the spectral shift function. In Stochastic processes, physics and geometry: new interplays, II (Leipzig, 1999), volume 29 of CMS Conf. Proc., pages 207-222. Amer. Math. Soc., Providence, RI, 2000.
  • 197
    • 84971137953 scopus 로고
    • On subordinacy and analysis of Schrödinger operators with singular endpoints
    • D. Gilbert. On subordinacy and analysis of Schrödinger operators with singular endpoints. Proc. Royal Soc. Edinburgh, 112A:213-229, 1989.
    • (1989) Proc. Royal Soc. Edinburgh , vol.112 A , pp. 213-229
    • Gilbert, D.1
  • 198
    • 0002280835 scopus 로고
    • On subordinacy and analysis of the spectrum of one-dimensional Schrödinger operators
    • D. Gilbert and D. Pearson. On subordinacy and analysis of the spectrum of one-dimensional Schrödinger operators. J. Math. Anal Appl., 128:30-56, 1987.
    • (1987) J. Math. Anal Appl , vol.128 , pp. 30-56
    • Gilbert, D.1    Pearson, D.2
  • 199
    • 85009417029 scopus 로고    scopus 로고
    • I. Gohberg and I. Feldman. Convolution Operators and Projection Methods for Their Solution. Amr. Math. Soc., Providence, R.I., 1974. [Russian original: Izdat. Nauka, Moscow, 1971].
    • I. Gohberg and I. Feldman. Convolution Operators and Projection Methods for Their Solution. Amr. Math. Soc., Providence, R.I., 1974. [Russian original: Izdat. "Nauka", Moscow, 1971].
  • 201
    • 84916764879 scopus 로고
    • The structure of the spectrum of the Schrödinger random difference operator
    • I. Y. Goldsheid. The structure of the spectrum of the Schrödinger random difference operator. Sov. Math. Dokl., 22:670-674, 1981.
    • (1981) Sov. Math. Dokl , vol.22 , pp. 670-674
    • Goldsheid, I.Y.1
  • 202
    • 34250283162 scopus 로고
    • A pure point spectrum of the stochastic one-dimensional Schrödinger operator
    • I. Y. Goldsheid, S. A. Molčanov, and L. Pastur. A pure point spectrum of the stochastic one-dimensional Schrödinger operator. Functional Anal. Appl., 11:1-10, 1977.
    • (1977) Functional Anal. Appl , vol.11 , pp. 1-10
    • Goldsheid, I.Y.1    Molčanov, S.A.2    Pastur, L.3
  • 203
    • 21344482002 scopus 로고
    • Anderson localization and the space-time characteristic of continuum states
    • G.-M. Graf. Anderson localization and the space-time characteristic of continuum states. J. Stat. Phys., 75(1-2):337-346, 1994.
    • (1994) J. Stat. Phys , vol.75 , Issue.1-2 , pp. 337-346
    • Graf, G.-M.1
  • 204
    • 0003287329 scopus 로고
    • Invariant means on topological groups and their applications
    • Van Nostrand Reinhold Co, New York
    • F. P. Greenleaf. Invariant means on topological groups and their applications. Van Nostrand Mathematical Studies, No. 16. Van Nostrand Reinhold Co., New York, 1969.
    • (1969) Van Nostrand Mathematical Studies , Issue.16
    • Greenleaf, F.P.1
  • 206
    • 85009418059 scopus 로고    scopus 로고
    • A. Grigor'yan. Stochastically complete manifolds. Dokl. Akad. Nauk SSSR, 290(3):534-537, 1986. [English translation: Soviet Math. Dokl., 34 (1987) no. 2, 310-313].
    • A. Grigor'yan. Stochastically complete manifolds. Dokl. Akad. Nauk SSSR, 290(3):534-537, 1986. [English translation: Soviet Math. Dokl., 34 (1987) no. 2, 310-313].
  • 208
    • 0000050373 scopus 로고
    • von Neumann spectra near zero
    • M. Gromov and M. A. Shubin. von Neumann spectra near zero. Geom. Funct. Anal., 1(4):375-404, 1991.
    • (1991) Geom. Funct. Anal , vol.1 , Issue.4 , pp. 375-404
    • Gromov, M.1    Shubin, M.A.2
  • 210
    • 85009425626 scopus 로고    scopus 로고
    • The modulus of continuity of the ids for random Schrödinger operators on metric graphs
    • To appear in
    • M. Gruber and I. Veselić. The modulus of continuity of the ids for random Schrödinger operators on metric graphs. To appear in Random Oper. Stochastic Equations.
    • Random Oper. Stochastic Equations
    • Gruber, M.1    Veselić, I.2
  • 211
    • 0002431814 scopus 로고    scopus 로고
    • Asymptotic of the density of states for the Schrödinger operator with periodic electric potential
    • B. Helffer and A. Mohamed. Asymptotic of the density of states for the Schrödinger operator with periodic electric potential. Duke Math. J., 92(1):1-60, 1998.
    • (1998) Duke Math. J , vol.92 , Issue.1 , pp. 1-60
    • Helffer, B.1    Mohamed, A.2
  • 212
    • 85009418067 scopus 로고    scopus 로고
    • A linear Wegner estimate for alloy type Schrödinger operators on metric graphs. http://www.arXiv.org/abs/math/ 0611609
    • To appear in
    • M. Helm and I. Veselić. A linear Wegner estimate for alloy type Schrödinger operators on metric graphs. http://www.arXiv.org/abs/math/ 0611609. To appear in J. Math. Phys.
    • J. Math. Phys
    • Helm, M.1    Veselić, I.2
  • 213
    • 0037145490 scopus 로고    scopus 로고
    • P. D. Hislop and F. Klopp. The integrated density of states for some random operators with nonsign definite potentials. J. Funct. Anal., 195(1):12-47, 2002. www.ma.utexas.edu/mp_arc, preprint no. 01-139 (2001).
    • P. D. Hislop and F. Klopp. The integrated density of states for some random operators with nonsign definite potentials. J. Funct. Anal., 195(1):12-47, 2002. www.ma.utexas.edu/mp_arc, preprint no. 01-139 (2001).
  • 214
    • 33745644487 scopus 로고    scopus 로고
    • P. D. Hislop, F. Klopp, and J. H. Schenker. Continuity with respect to disorder of the integrated density of states. Illinois J. Math., 49(3):893-904 (electronic), 2005.
    • P. D. Hislop, F. Klopp, and J. H. Schenker. Continuity with respect to disorder of the integrated density of states. Illinois J. Math., 49(3):893-904 (electronic), 2005.
  • 217
    • 10844231509 scopus 로고    scopus 로고
    • Stochastic analysis on manifolds
    • of, American Mathematical Society, Providence, RI
    • E. P. Hsu. Stochastic analysis on manifolds, volume 38 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 2002.
    • (2002) Graduate Studies in Mathematics , vol.38
    • Hsu, E.P.1
  • 218
    • 31344455913 scopus 로고    scopus 로고
    • Bounds on the spectral shift function and the density of states
    • D. Hundertmark, R. Killip, S. Nakamura, P. Stollmann, and I. Veselić. Bounds on the spectral shift function and the density of states. Comm. Math. Phys., 262(2):489-503, 2006. http://arxiv.org/math-ph/ 0412078.
    • (2006) Comm. Math. Phys , vol.262 , Issue.2 , pp. 489-503
    • Hundertmark, D.1    Killip, R.2    Nakamura, S.3    Stollmann, P.4    Veselić, I.5
  • 220
    • 85009418064 scopus 로고    scopus 로고
    • D. Hundertmark, W. Kirsch, and S. Warzel. Classical magnetic Lifshits tails in three space dimensions: impurity potentials with slow anisotropic decay. Markov Process. Related Fields, 9(4):651-660, 2003. http://www.arxiv.org/abs/math-ph/0212078, proceedings of the conference Aspects Mathématiques des Systèmes Aléatoires et de la Mécanique Statistique, May 2002, Marseille.
    • D. Hundertmark, W. Kirsch, and S. Warzel. Classical magnetic Lifshits tails in three space dimensions: impurity potentials with slow anisotropic decay. Markov Process. Related Fields, 9(4):651-660, 2003. http://www.arxiv.org/abs/math-ph/0212078, proceedings of the conference Aspects Mathématiques des Systèmes Aléatoires et de la Mécanique Statistique, May 2002, Marseille.
  • 221
    • 0036436441 scopus 로고    scopus 로고
    • p-bound on the Krein spectral shift function
    • p-bound on the Krein spectral shift function. J. Anal. Math., 87:199-208, 2002. http://www.ma.utexas.edu/mp-arc/c/00/00-370.ps.gz.
    • (2002) J. Anal. Math , vol.87 , pp. 199-208
    • Hundertmark, D.1    Simon, B.2
  • 222
    • 3142685163 scopus 로고    scopus 로고
    • A diamagnetic inequality for semigroup differences
    • D. Hundertmark and B. Simon. A diamagnetic inequality for semigroup differences. J. Reine Angew. Math., 571:107-130, 2004.
    • (2004) J. Reine Angew. Math , vol.571 , pp. 107-130
    • Hundertmark, D.1    Simon, B.2
  • 223
    • 0035536778 scopus 로고    scopus 로고
    • The absolute continuity of the integrated density of states for magnetic Schrödinger operators with certain unbounded random potentials
    • T. Hupfer, H. Leschke, P. Müller, and S. Warzel. The absolute continuity of the integrated density of states for magnetic Schrödinger operators with certain unbounded random potentials. Comm. Math. Phys., 221(2):229-254, 2001.
    • (2001) Comm. Math. Phys , vol.221 , Issue.2 , pp. 229-254
    • Hupfer, T.1    Leschke, H.2    Müller, P.3    Warzel, S.4
  • 224
    • 0035733037 scopus 로고    scopus 로고
    • Existence and uniqueness of the integrated density of states for Schrödinger operators with magnetic fields and unbounded random potentials
    • T. Hupfer, H. Leschke, P. Müller, and S. Warzel. Existence and uniqueness of the integrated density of states for Schrödinger operators with magnetic fields and unbounded random potentials. Rev. Math. Phys., 13(12):1547-1581, 2001.
    • (2001) Rev. Math. Phys , vol.13 , Issue.12 , pp. 1547-1581
    • Hupfer, T.1    Leschke, H.2    Müller, P.3    Warzel, S.4
  • 225
    • 0033235597 scopus 로고    scopus 로고
    • Poissonian obstacles with Gaussian walls discriminate between classical and quantum Lifshits tailing in magnetic fields
    • T. Hupfer, H. Leschke, and S. Warzel. Poissonian obstacles with Gaussian walls discriminate between classical and quantum Lifshits tailing in magnetic fields. J. Statist. Phys., 97(3-4):725-750, 1999.
    • (1999) J. Statist. Phys , vol.97 , Issue.3-4 , pp. 725-750
    • Hupfer, T.1    Leschke, H.2    Warzel, S.3
  • 226
    • 85009354296 scopus 로고    scopus 로고
    • T. Hupfer, H. Leschke, and S. Warzel. The multiformity of Lifshits tails caused by random Landau Hamiltonians with repulsive impurity potentials of different decay at infinity. In Differential equations and mathematical physics (Birmingham, 1999), 16 of AMS/IP Stud. Adv. Math., pages 233-247. Amer. Math. Soc., Providence, RI, 2000.
    • T. Hupfer, H. Leschke, and S. Warzel. The multiformity of Lifshits tails caused by random Landau Hamiltonians with repulsive impurity potentials of different decay at infinity. In Differential equations and mathematical physics (Birmingham, 1999), volume 16 of AMS/IP Stud. Adv. Math., pages 233-247. Amer. Math. Soc., Providence, RI, 2000.
  • 227
    • 0035540634 scopus 로고    scopus 로고
    • Upper bounds on the density of states of single Landau levels broadened by Gaussian random potentials
    • T. Hupfer, H. Leschke, and S. Warzel. Upper bounds on the density of states of single Landau levels broadened by Gaussian random potentials. J. Math. Phys., 42(12):5626-5641, 2001.
    • (2001) J. Math. Phys , vol.42 , Issue.12 , pp. 5626-5641
    • Hupfer, T.1    Leschke, H.2    Warzel, S.3
  • 228
    • 0005812514 scopus 로고
    • On the Hellmann-Feynman theorem and the variation of zeros of certain special functions
    • M. Ismail and R. Zhang. On the Hellmann-Feynman theorem and the variation of zeros of certain special functions. Adv. Appl Math., 9:439-446, 1988.
    • (1988) Adv. Appl Math , vol.9 , pp. 439-446
    • Ismail, M.1    Zhang, R.2
  • 229
    • 0034310145 scopus 로고    scopus 로고
    • Corrugated surfaces and a.c. spectrum
    • V. Jakšić and Y. Last. Corrugated surfaces and a.c. spectrum. Rev. Math. Phys., 12(11):1465-1503, 2000.
    • (2000) Rev. Math. Phys , vol.12 , Issue.11 , pp. 1465-1503
    • Jakšić, V.1    Last, Y.2
  • 230
    • 0034349435 scopus 로고    scopus 로고
    • Spectral structure of Anderson type Hamiltonians
    • V. Jakśić and Y. Last. Spectral structure of Anderson type Hamiltonians. Invent. Math., 141(3):561-577, 2000.
    • (2000) Invent. Math , vol.141 , Issue.3 , pp. 561-577
    • Jakśić, V.1    Last, Y.2
  • 231
    • 0035531307 scopus 로고    scopus 로고
    • Surface states and spectra
    • V. Jakšić and Y. Last. Surface states and spectra. Comm. Math. Phys., 218(3): 459-477, 2001.
    • (2001) Comm. Math. Phys , vol.218 , Issue.3 , pp. 459-477
    • Jakšić, V.1    Last, Y.2
  • 232
    • 37149041224 scopus 로고    scopus 로고
    • Scattering from subspace potentials for Schrödinger operators on graphs
    • V. Jakšić and Y. Last. Scattering from subspace potentials for Schrödinger operators on graphs. Markov Process. Related Fields, 9(4):661-674, 2003.
    • (2003) Markov Process. Related Fields , vol.9 , Issue.4 , pp. 661-674
    • Jakšić, V.1    Last, Y.2
  • 233
    • 33744820326 scopus 로고    scopus 로고
    • Simplicity of singular spectrum in Anderson-type Hamiltonians
    • V. Jakšić and Y. Last. Simplicity of singular spectrum in Anderson-type Hamiltonians. Duke Math. J., 133(1):185-204, 2006.
    • (2006) Duke Math. J , vol.133 , Issue.1 , pp. 185-204
    • Jakšić, V.1    Last, Y.2
  • 236
    • 0000423029 scopus 로고
    • The rotation number for almost periodic potentials
    • R. Johnson and J. Moser. The rotation number for almost periodic potentials. Comm. Math. Phys., 84(3):403-438, 1982.
    • (1982) Comm. Math. Phys , vol.84 , Issue.3 , pp. 403-438
    • Johnson, R.1    Moser, J.2
  • 237
    • 0742303987 scopus 로고    scopus 로고
    • A proof of the gap labeling conjecture
    • J. Kaminker and I. Putnam. A proof of the gap labeling conjecture. Michigan Math. J., 51(3):537-546, 2003.
    • (2003) Michigan Math. J , vol.51 , Issue.3 , pp. 537-546
    • Kaminker, J.1    Putnam, I.2
  • 238
    • 0039598697 scopus 로고    scopus 로고
    • Spectral gaps of Schrödinger operators on hyperbolic space
    • L. Karp and N. Peyerimhoff. Spectral gaps of Schrödinger operators on hyperbolic space. Math. Nachr., 217:105-124, 2000.
    • (2000) Math. Nachr , vol.217 , pp. 105-124
    • Karp, L.1    Peyerimhoff, N.2
  • 240
    • 21844484789 scopus 로고
    • Noncommutative geometry of tilings and gap labelling
    • J. Kellendonk. Noncommutative geometry of tilings and gap labelling. Rev. Math. Phys., 7(7):1133-1180, 1995.
    • (1995) Rev. Math. Phys , vol.7 , Issue.7 , pp. 1133-1180
    • Kellendonk, J.1
  • 241
    • 0036002351 scopus 로고    scopus 로고
    • Edge current channels and Chern numbers in the integer quantum Hall effect
    • J. Kellendonk, T. Richter, and H. Schulz-Baldes. Edge current channels and Chern numbers in the integer quantum Hall effect. Rev. Math. Phys., 14(1):87-119, 2002.
    • (2002) Rev. Math. Phys , vol.14 , Issue.1 , pp. 87-119
    • Kellendonk, J.1    Richter, T.2    Schulz-Baldes, H.3
  • 242
    • 0003222070 scopus 로고
    • Percolation theory for mathematicians
    • of, Birkhäuser, Boston
    • H. Kesten. Percolation theory for mathematicians, volume 2 of Progress in Probability and Statistics. Birkhäuser, Boston, 1982.
    • (1982) Progress in Probability and Statistics , vol.2
    • Kesten, H.1
  • 243
    • 33847326432 scopus 로고    scopus 로고
    • Eigenfunction statistics in the localized Anderson model
    • R. Killip and F. Nakano. Eigenfunction statistics in the localized Anderson model. Ann. Henri Poincaré, 8(1):27-36, 2007. http://www.ma.utexas.edu/mp_arc/c/06/06-150.ps.gz.
    • (2007) Ann. Henri Poincaré , vol.8 , Issue.1 , pp. 27-36
    • Killip, R.1    Nakano, F.2
  • 244
    • 0000605687 scopus 로고
    • Localized states of a binary alloy
    • S. Kirkpatrick and T. P. Eggarter. Localized states of a binary alloy. Phys. Rev. B, 6:3598, 1972.
    • (1972) Phys. Rev. B , vol.6 , pp. 3598
    • Kirkpatrick, S.1    Eggarter, T.P.2
  • 246
    • 0039169600 scopus 로고
    • Small perturbations and the eigenvalues of the Laplacian on large bounded domains
    • W. Kirsch. Small perturbations and the eigenvalues of the Laplacian on large bounded domains. Proc. Am. Math. Soc., 101:509-512, 1987.
    • (1987) Proc. Am. Math. Soc , vol.101 , pp. 509-512
    • Kirsch, W.1
  • 247
    • 0000818766 scopus 로고
    • Random Schrödinger operators
    • H. Holden and A. Jensen, editors, Schrödinger Operators, Berlin, Springer
    • W. Kirsch. Random Schrödinger operators. In H. Holden and A. Jensen, editors, Schrödinger Operators, Lecture Notes in Physics, 345, Berlin, 1989. Springer.
    • (1989) Lecture Notes in Physics , vol.345
    • Kirsch, W.1
  • 248
    • 31344475155 scopus 로고
    • The stability of the density of states of Schrödinger operator under very small perturbations
    • W. Kirsch. The stability of the density of states of Schrödinger operator under very small perturbations. Integral Equations Operator Theory, 12(3):383-391, 1989.
    • (1989) Integral Equations Operator Theory , vol.12 , Issue.3 , pp. 383-391
    • Kirsch, W.1
  • 249
    • 0030093716 scopus 로고    scopus 로고
    • Wegner estimates and Anderson localization for alloy-type potentials
    • W. Kirsch. Wegner estimates and Anderson localization for alloy-type potentials. Math. Z., 221:507-512, 1996.
    • (1996) Math. Z , vol.221 , pp. 507-512
    • Kirsch, W.1
  • 250
    • 4043133956 scopus 로고    scopus 로고
    • Scattering theory for sparse random potentials
    • W. Kirsch. Scattering theory for sparse random potentials. Random Oper. Stochastic Equations, 10(4):329-334, 2002.
    • (2002) Random Oper. Stochastic Equations , vol.10 , Issue.4 , pp. 329-334
    • Kirsch, W.1
  • 251
    • 33745618142 scopus 로고    scopus 로고
    • The band-edge behavior of the density of surfacic states
    • 84
    • W. Kirsch and F. Klopp. The band-edge behavior of the density of surfacic states. Math. Phys. Anal Geom., 8(4):315-360 (2006), 2005.
    • (2006) Math. Phys. Anal Geom , vol.315-360 , pp. 2005
    • Kirsch, W.1    Klopp, F.2
  • 252
    • 0000505933 scopus 로고
    • Absence of absolutely continuous spectrum for some one-dimensional random but deterministic Schrödinger operators
    • W. Kirsch, S.-I. Kotani, and B. Simon. Absence of absolutely continuous spectrum for some one-dimensional random but deterministic Schrödinger operators. Ann. Inst. Henri Poincaré, 42:383-406, 1985.
    • (1985) Ann. Inst. Henri Poincaré , vol.42 , pp. 383-406
    • Kirsch, W.1    Kotani, S.-I.2    Simon, B.3
  • 253
    • 0034362698 scopus 로고    scopus 로고
    • Anderson model with decaying randomness: Mobility edge
    • W. Kirsch, M. Krishna, and J. Obermeit. Anderson model with decaying randomness: mobility edge. Math. Z., 235(3):421-433, 2000.
    • (2000) Math. Z , vol.235 , Issue.3 , pp. 421-433
    • Kirsch, W.1    Krishna, M.2    Obermeit, J.3
  • 254
    • 0000059648 scopus 로고
    • On the density of states of Schrödinger operators with a random potential
    • W. Kirsch and F. Martinelli. On the density of states of Schrödinger operators with a random potential. J. Phys. A: Math. Gen., 15:2139-2156, 1982.
    • (1982) J. Phys. A: Math. Gen , vol.15 , pp. 2139-2156
    • Kirsch, W.1    Martinelli, F.2
  • 255
    • 0000112074 scopus 로고
    • On the ergodic properties of the spectrum of general random operators
    • W. Kirsch and F. Martinelli. On the ergodic properties of the spectrum of general random operators. J. Reine Angew. Math., 334:141-156, 1982.
    • (1982) J. Reine Angew. Math , vol.334 , pp. 141-156
    • Kirsch, W.1    Martinelli, F.2
  • 256
    • 0001207353 scopus 로고
    • On the spectrum of Schrödinger operators with a random potential
    • W. Kirsch and F. Martinelli. On the spectrum of Schrödinger operators with a random potential. Commun. Math. Phys., 85:329-350, 1982.
    • (1982) Commun. Math. Phys , vol.85 , pp. 329-350
    • Kirsch, W.1    Martinelli, F.2
  • 257
    • 0002359044 scopus 로고
    • Large deviations and Lifshitz singularity of the integrated density of states of random Hamitonians
    • W. Kirsch and F. Martinelli. Large deviations and Lifshitz singularity of the integrated density of states of random Hamitonians. Commun. Math. Phys., 89:27-40, 1983.
    • (1983) Commun. Math. Phys , vol.89 , pp. 27-40
    • Kirsch, W.1    Martinelli, F.2
  • 258
    • 0010964692 scopus 로고
    • On the essential selfadjointness of stochastic Schrödinger operators
    • W. Kirsch and F. Martinelli. On the essential selfadjointness of stochastic Schrödinger operators. Duke Math. J., 50:1255-1260, 1983.
    • (1983) Duke Math. J , vol.50 , pp. 1255-1260
    • Kirsch, W.1    Martinelli, F.2
  • 260
    • 32944463108 scopus 로고    scopus 로고
    • Spectral properties of the Laplacian on bondpercolation graphs
    • W. Kirsch and P. Müller. Spectral properties of the Laplacian on bondpercolation graphs. Math. Zeit, 252(4):899-916, 2006. http://www.arXiv.org/abs/math-ph/0407047.
    • (2006) Math. Zeit , vol.252 , Issue.4 , pp. 899-916
    • Kirsch, W.1    Müller, P.2
  • 261
    • 0034346376 scopus 로고    scopus 로고
    • Strong magnetic field asymptotics of the integrated density of states for a random 3D Schrödinger operator
    • W. Kirsch and G. D. Raikov. Strong magnetic field asymptotics of the integrated density of states for a random 3D Schrödinger operator. Ann. Henri Poincaré, 1(5):801-821, 2000.
    • (2000) Ann. Henri Poincaré , vol.1 , Issue.5 , pp. 801-821
    • Kirsch, W.1    Raikov, G.D.2
  • 262
    • 0002351434 scopus 로고
    • Lifshitz tails for periodic plus random potentials
    • W. Kirsch and B. Simon. Lifshitz tails for periodic plus random potentials. J. Stat. Phys., 42:799-808, 1986.
    • (1986) J. Stat. Phys , vol.42 , pp. 799-808
    • Kirsch, W.1    Simon, B.2
  • 264
    • 0040350235 scopus 로고    scopus 로고
    • Anderson localization for random Schrödinger operators with long range interactions
    • W. Kirsch, P. Stollmann, and G. Stolz. Anderson localization for random Schrödinger operators with long range interactions. Comm. Math. Phys., 195(3):495-507, 1998.
    • (1998) Comm. Math. Phys , vol.195 , Issue.3 , pp. 495-507
    • Kirsch, W.1    Stollmann, P.2    Stolz, G.3
  • 265
    • 84868025903 scopus 로고    scopus 로고
    • Localization for random perturbations of periodic Schrödinger operators
    • W. Kirsch, P. Stollmann, and G. Stolz. Localization for random perturbations of periodic Schrödinger operators. Random Oper. Stochastic Equations, 6(3):241-268, 1998. http://www.ma.utexas.edu/mp.arc/c/96/96-648. ps.gz.
    • (1998) Random Oper. Stochastic Equations , vol.6 , Issue.3 , pp. 241-268
    • Kirsch, W.1    Stollmann, P.2    Stolz, G.3
  • 267
    • 85009419598 scopus 로고    scopus 로고
    • W. Kirsch and I. Veselić. Existence of the density of states for one-dimensional alloy-type potentials with small support. In Mathematical Results in Quantum Mechanics (Taxco, Mexico, 2001), 307 of Contemp. Math., pages 171-176. Amer. Math. Soc., Providence, RI, 2002. http://arxiv.org/abs/math-ph/0204030.
    • W. Kirsch and I. Veselić. Existence of the density of states for one-dimensional alloy-type potentials with small support. In Mathematical Results in Quantum Mechanics (Taxco, Mexico, 2001), volume 307 of Contemp. Math., pages 171-176. Amer. Math. Soc., Providence, RI, 2002. http://arxiv.org/abs/math-ph/0204030.
  • 268
    • 0036475391 scopus 로고    scopus 로고
    • Wegner estimate for sparse and other generalized alloy type potentials
    • 131-146, mp.arc-bin/02-143
    • W. Kirsch and I. Veselić. Wegner estimate for sparse and other generalized alloy type potentials. Proc. Indian Acad. Sci. Math. Sci., 112(1):131-146, 2002. www.ias.ac.in/mathsci/,mp.arc-bin/02-143.
    • (2002) Proc. Indian Acad. Sci. Math. Sci , vol.112 , Issue.1
    • Kirsch, W.1    Veselić, I.2
  • 269
    • 28644449428 scopus 로고    scopus 로고
    • Anderson localization and lifshits tails for random surface potentials
    • W. Kirsch and S. Warzel. Anderson localization and lifshits tails for random surface potentials. J. Funct. Anal., 230(1):222-250, 2006. http://arxiv.org/abs/math-ph/0412079.
    • (2006) J. Funct. Anal , vol.230 , Issue.1 , pp. 222-250
    • Kirsch, W.1    Warzel, S.2
  • 270
    • 28644449428 scopus 로고    scopus 로고
    • Lifshits tails caused by anisotropic decay: The emergence of a quantum-classical regime
    • W. Kirsch and S. Warzel. Lifshits tails caused by anisotropic decay: the emergence of a quantum-classical regime. J. Funct. Anal., 230(1):222-250, 2006. http://www.arxiv.org/math-ph/0310033.
    • (2006) J. Funct. Anal , vol.230 , Issue.1 , pp. 222-250
    • Kirsch, W.1    Warzel, S.2
  • 273
    • 0242370757 scopus 로고    scopus 로고
    • Discontinuities of the integrated density of states for random operators on Delone sets
    • S. Klassert, D. Lenz, and P. Stollmann. Discontinuities of the integrated density of states for random operators on Delone sets. Comm. Math. Phys., 241(2-3): 235-243, 2003. http://arXiv.org/math-ph/0208027.
    • (2003) Comm. Math. Phys , vol.241 , Issue.2-3 , pp. 235-243
    • Klassert, S.1    Lenz, D.2    Stollmann, P.3
  • 275
    • 0034368999 scopus 로고    scopus 로고
    • Lifshitz asymptotics and localization for random quantum waveguides
    • F. Kleespies and P. Stollmann. Lifshitz asymptotics and localization for random quantum waveguides. Rev. Math. Phys., 12(10):1345-1365, 2000.
    • (2000) Rev. Math. Phys , vol.12 , Issue.10 , pp. 1345-1365
    • Kleespies, F.1    Stollmann, P.2
  • 276
    • 0030539477 scopus 로고    scopus 로고
    • Spreading of wave packets in the Anderson model on the Bethe lattice
    • A. Klein. Spreading of wave packets in the Anderson model on the Bethe lattice. Comm. Math. Phys., 177(3):755-773, 1996.
    • (1996) Comm. Math. Phys , vol.177 , Issue.3 , pp. 755-773
    • Klein, A.1
  • 277
    • 0000120387 scopus 로고    scopus 로고
    • Extended states in the Anderson model on the Bethe lattice
    • A. Klein. Extended states in the Anderson model on the Bethe lattice. Adv. Math., 133(1): 163-184, 1998.
    • (1998) Adv. Math , vol.133 , Issue.1 , pp. 163-184
    • Klein, A.1
  • 278
    • 3543068115 scopus 로고    scopus 로고
    • A general framework for localization of classical waves. II. Random media
    • A. Klein and A. Koines. A general framework for localization of classical waves. II. Random media. Math. Phys. Anal Geom., 7(2): 151-185, 2004. http://www.ma.utexas.edu/mp_arc/c/02/02-470.pdf.
    • (2004) Math. Phys. Anal Geom , vol.7 , Issue.2 , pp. 151-185
    • Klein, A.1    Koines, A.2
  • 279
    • 33644519013 scopus 로고    scopus 로고
    • Simplicity of eigenvalues in the Anderson model
    • A. Klein and S. Molchanov. Simplicity of eigenvalues in the Anderson model. J. Stat. Phys., 122(1):95-99, 2006.
    • (2006) J. Stat. Phys , vol.122 , Issue.1 , pp. 95-99
    • Klein, A.1    Molchanov, S.2
  • 280
    • 0242639458 scopus 로고
    • Localization for semiclassical continuous random Schrödinger operators II: The random displacement model
    • F. Klopp. Localization for semiclassical continuous random Schrödinger operators II: The random displacement model. Helv. Phys. Acta, 66:810-841, 1993.
    • (1993) Helv. Phys. Acta , vol.66 , pp. 810-841
    • Klopp, F.1
  • 281
    • 0011686957 scopus 로고
    • d): Un modèle semi-classique
    • d): un modèle semi-classique. Ann. Inst. Fourier (Grenoble), 45(1):265-316, 1995.
    • (1995) Ann. Inst. Fourier (Grenoble) , vol.45 , Issue.1 , pp. 265-316
    • Klopp, F.1
  • 282
    • 21844521255 scopus 로고
    • Localization for some continuous random Schrödinger operators
    • F. Klopp. Localization for some continuous random Schrödinger operators. Commun. Math. Phys., 167:553-569, 1995.
    • (1995) Commun. Math. Phys , vol.167 , pp. 553-569
    • Klopp, F.1
  • 283
    • 0033148063 scopus 로고    scopus 로고
    • Internal Lifshits tails for random perturbations of periodic Schrödinger operators
    • F. Klopp. Internal Lifshits tails for random perturbations of periodic Schrödinger operators. Duke Math. J., 98(2):335-396, 1999.
    • (1999) Duke Math. J , vol.98 , Issue.2 , pp. 335-396
    • Klopp, F.1
  • 284
    • 0034386766 scopus 로고    scopus 로고
    • Precise high energy asymptotics for the integrated density of states of an unbounded random Jacobi matrix
    • F. Klopp. Precise high energy asymptotics for the integrated density of states of an unbounded random Jacobi matrix. Rev. Math. Phys., 12(4):575-620, 2000.
    • (2000) Rev. Math. Phys , vol.12 , Issue.4 , pp. 575-620
    • Klopp, F.1
  • 285
    • 0037715328 scopus 로고    scopus 로고
    • Une remarque à propos des asymptotiques de Lifshitz internes
    • F. Klopp. Une remarque à propos des asymptotiques de Lifshitz internes. C.R. Math. Acad. Sci. Paris, 335(1):87-92, 2002.
    • (2002) C.R. Math. Acad. Sci. Paris , vol.335 , Issue.1 , pp. 87-92
    • Klopp, F.1
  • 286
    • 0036882746 scopus 로고    scopus 로고
    • Weak disorder localization and Lifshitz tails
    • F. Klopp. Weak disorder localization and Lifshitz tails. Comm. Math. Phys., 232(1):125-155, 2002.
    • (2002) Comm. Math. Phys , vol.232 , Issue.1 , pp. 125-155
    • Klopp, F.1
  • 287
    • 0036025587 scopus 로고    scopus 로고
    • Weak disorder localization and Lifshitz tails: Continuous Hamiltonians
    • F. Klopp. Weak disorder localization and Lifshitz tails: continuous Hamiltonians. Ann. Henri Poincaré, 3(4):711-737, 2002.
    • (2002) Ann. Henri Poincaré , vol.3 , Issue.4 , pp. 711-737
    • Klopp, F.1
  • 288
    • 0033450317 scopus 로고    scopus 로고
    • Lifshitz tails for random Schrödinger operators with negative singular Poisson potential
    • F. Klopp and L. Pastur. Lifshitz tails for random Schrödinger operators with negative singular Poisson potential. Commun. Math. Phys., 206(1):57-103, 1999.
    • (1999) Commun. Math. Phys , vol.206 , Issue.1 , pp. 57-103
    • Klopp, F.1    Pastur, L.2
  • 289
    • 33748545669 scopus 로고    scopus 로고
    • Lifshitz tails in constant magnetic fields
    • F. Klopp and G. Raikov. Lifshitz tails in constant magnetic fields. Comm. Math. Phys., 267(3):669-701, 2006.
    • (2006) Comm. Math. Phys , vol.267 , Issue.3 , pp. 669-701
    • Klopp, F.1    Raikov, G.2
  • 290
    • 85009361045 scopus 로고    scopus 로고
    • Internal Lifshitz tails for random Schrödinger operators
    • Int. Press, Boston, MA
    • F. Klopp and T. Wolff. Internal Lifshitz tails for random Schrödinger operators. In XIIIth International Congress on Mathematical Physics (London, 2000), pages 425-433. Int. Press, Boston, MA, 2001. http://www.ma.utexas.edu/mp_arc/c/00/00-390.ps.gz.
    • (2001) XIIIth International Congress on Mathematical Physics (London, 2000) , pp. 425-433
    • Klopp, F.1    Wolff, T.2
  • 291
    • 0036942041 scopus 로고    scopus 로고
    • Lifshitz tails for 2-dimensional random Schrödinger operators
    • Dedicated to the memory of Tom Wolff
    • F. Klopp and T. Wolff. Lifshitz tails for 2-dimensional random Schrödinger operators. J. Anal Math., 88:63-147, 2002. Dedicated to the memory of Tom Wolff.
    • (2002) J. Anal Math , vol.88 , pp. 63-147
    • Klopp, F.1    Wolff, T.2
  • 292
    • 0001844778 scopus 로고
    • Periodic Schrödinger operators on a manifold
    • T. Kobayashi, K. Ono, and T. Sunada,. Periodic Schrödinger operators on a manifold. Forum Math., 1(1):69-79, 1989.
    • (1989) Forum Math , vol.1 , Issue.1 , pp. 69-79
    • Kobayashi, T.1    Ono, K.2    Sunada, T.3
  • 293
    • 85009361043 scopus 로고    scopus 로고
    • V. Kostrykin. The spectral shift function and its applications to random schrödinger operators, 1999. Habilitation thesis, RWTH Aachen, 1999.
    • V. Kostrykin. The spectral shift function and its applications to random schrödinger operators, 1999. Habilitation thesis, RWTH Aachen, 1999.
  • 294
    • 0006978673 scopus 로고    scopus 로고
    • Concavity of eigenvalue sums and the spectral shift function
    • V. Kostrykin. Concavity of eigenvalue sums and the spectral shift function. J. Funct. Anal., 176(1):100-114, 2000.
    • (2000) J. Funct. Anal , vol.176 , Issue.1 , pp. 100-114
    • Kostrykin, V.1
  • 296
    • 0033467794 scopus 로고    scopus 로고
    • Scattering theory approach to random Schrödinger operators in one dimension
    • V. Kostrykin and R. Schrader. Scattering theory approach to random Schrödinger operators in one dimension. Rev. Math. Phys., 11(2):187-242, 1999.
    • (1999) Rev. Math. Phys , vol.11 , Issue.2 , pp. 187-242
    • Kostrykin, V.1    Schrader, R.2
  • 297
    • 0034373969 scopus 로고    scopus 로고
    • The density of states and the spectral shift density of random Schrödinger operators
    • V. Kostrykin and R. Schrader. The density of states and the spectral shift density of random Schrödinger operators. Rev. Math. Phys., 12(6):807-847, 2000.
    • (2000) Rev. Math. Phys , vol.12 , Issue.6 , pp. 807-847
    • Kostrykin, V.1    Schrader, R.2
  • 298
    • 0035578191 scopus 로고    scopus 로고
    • Regularity of the surface density of states
    • V. Kostrykin and R. Schrader. Regularity of the surface density of states. J. Funct. Anal., 187(1):227-246, 2001.
    • (2001) J. Funct. Anal , vol.187 , Issue.1 , pp. 227-246
    • Kostrykin, V.1    Schrader, R.2
  • 299
  • 300
    • 85009419599 scopus 로고    scopus 로고
    • V. Kostrykin and I. Veselić. Wegner estimate for indefinite Anderson potentials: some recent results and applications. In K. R. Ito, editor, Renormalization Group Methods in Mathematical Sciences (Kyoto, 2001), 1275 of Lecture Notes of Res. Inst, of Math. Sciences, pages 65-84, 2002.
    • V. Kostrykin and I. Veselić. Wegner estimate for indefinite Anderson potentials: some recent results and applications. In K. R. Ito, editor, Renormalization Group Methods in Mathematical Sciences (Kyoto, 2001), volume 1275 of Lecture Notes of Res. Inst, of Math. Sciences, pages 65-84, 2002.
  • 301
    • 28644440546 scopus 로고    scopus 로고
    • On the Lipschitz continuity of the integrated density of states for sign-indefinite potentials
    • V. Kostrykin and I. Veselić. On the Lipschitz continuity of the integrated density of states for sign-indefinite potentials. Math. Z., 252(2):367-392, 2006. http://arXiv.org/math-ph/0408013.
    • (2006) Math. Z , vol.252 , Issue.2 , pp. 367-392
    • Kostrykin, V.1    Veselić, I.2
  • 302
    • 0242520920 scopus 로고
    • On asymptotic behavior of the spectrum of a one-dimensional hamiltonian with a certain coefficient
    • S. Kotani. On asymptotic behavior of the spectrum of a one-dimensional hamiltonian with a certain coefficient. Publ. Res. Inst. Math. Sci Kyoto. Univ., 12:447-492, 1976.
    • (1976) Publ. Res. Inst. Math. Sci Kyoto. Univ , vol.12 , pp. 447-492
    • Kotani, S.1
  • 303
    • 77956813930 scopus 로고
    • Ljapunov indices determine absolutely continuous spectra of stationary random one-dimensional Schrödinger operators
    • North-Holland, Amsterdam
    • S. Kotani. Ljapunov indices determine absolutely continuous spectra of stationary random one-dimensional Schrödinger operators. In Stochastic analysis (Katata/Kyoto, 1982), pages 225-247. North-Holland, Amsterdam, 1984.
    • (1984) Stochastic analysis (Katata/Kyoto, 1982) , pp. 225-247
    • Kotani, S.1
  • 304
    • 0000328340 scopus 로고
    • Lyapunov exponents and spectra for one-dimensional random Schrödinger operators
    • Amer. Math. Soc, Providence, R.I
    • S. Kotani. Lyapunov exponents and spectra for one-dimensional random Schrödinger operators. In Random matrices and their applications (Brunswick, 1984), Pages 277-286. Amer. Math. Soc., Providence, R.I., 1986.
    • (1986) Random matrices and their applications (Brunswick, 1984) , pp. 277-286
    • Kotani, S.1
  • 305
    • 0031271826 scopus 로고    scopus 로고
    • Generalized Floquet theory for stationary Schrödinger operators in one dimension
    • S. Kotani. Generalized Floquet theory for stationary Schrödinger operators in one dimension. Chaos Solitons Fractals, 8(11):1817-1854, 1997.
    • (1997) Chaos Solitons Fractals , vol.8 , Issue.11 , pp. 1817-1854
    • Kotani, S.1
  • 306
    • 34250100229 scopus 로고
    • Localization in general one-dimensional random systems. II. Continuum Schrödinger operators
    • S. Kotani and B. Simon. Localization in general one-dimensional random systems. II. Continuum Schrödinger operators. Comm. Math. Phys., 112(1):103-119, 1987.
    • (1987) Comm. Math. Phys , vol.112 , Issue.1 , pp. 103-119
    • Kotani, S.1    Simon, B.2
  • 307
    • 14544291875 scopus 로고
    • A certain projection method of solving operator equations in a Banach space
    • A. V. Kozak. A certain projection method of solving operator equations in a Banach space. Dokl. Akad. Nauk SSSR, 211:1042-1045, 1973.
    • (1973) Dokl. Akad. Nauk SSSR , vol.211 , pp. 1042-1045
    • Kozak, A.V.1
  • 308
    • 0039005600 scopus 로고
    • A local principle in the theory of projection methods
    • A. V. Kozak. A local principle in the theory of projection methods. Dokl Akad. Nauk SSSR, 212:1287-1289, 1973.
    • (1973) Dokl Akad. Nauk SSSR , vol.212 , pp. 1287-1289
    • Kozak, A.V.1
  • 309
    • 85009390037 scopus 로고    scopus 로고
    • A. V. Kozak. On the reduction method for multidimensional discrete convolutions. Mat. Issled., 8(3(29)):157-160, 184, 1973.
    • A. V. Kozak. On the reduction method for multidimensional discrete convolutions. Mat. Issled., 8(3(29)):157-160, 184, 1973.
  • 310
    • 34250278441 scopus 로고
    • Projection methods for the solution of two-dimensional singular equations on a torus
    • A. V. Kozak and I. B. Simonenko. Projection methods for the solution of two-dimensional singular equations on a torus. Funktsional. Anal i Prilozhen., 12(1):74-75, 1978.
    • (1978) Funktsional. Anal i Prilozhen , vol.12 , Issue.1 , pp. 74-75
    • Kozak, A.V.1    Simonenko, I.B.2
  • 311
    • 3042728693 scopus 로고
    • Projection methods for solving multidimensional discrete convolution equations
    • 212
    • A. V. Kozak and I. B. Simonenko. Projection methods for solving multidimensional discrete convolution equations. Sibirsk. Mat. Zh., 21(2):119-127, 237, 1980.
    • (1980) Sibirsk. Mat. Zh , vol.119-127 , pp. 237
    • Kozak, A.V.1    Simonenko, I.B.2
  • 313
    • 85009390030 scopus 로고    scopus 로고
    • U. Krengel. Ergodic Theorems. Studies in Mathematics. Walter de Gruyter, 1985.
    • U. Krengel. Ergodic Theorems. Studies in Mathematics. Walter de Gruyter, 1985.
  • 314
    • 85009401124 scopus 로고    scopus 로고
    • Continuity of integrated density of states - independent randomness
    • math-ph/0609040
    • M. Krishna. Continuity of integrated density of states - independent randomness. math-ph/0609040.
    • Krishna, M.1
  • 315
    • 0002512318 scopus 로고
    • Anderson Model with decaying randomness - extended states
    • M. Krishna. Anderson Model with decaying randomness - extended states. Proc. Indian. Acad. Sci. (MathSci.), 100(4):285-294, 1990.
    • (1990) Proc. Indian. Acad. Sci. (MathSci.) , vol.100 , Issue.4 , pp. 285-294
    • Krishna, M.1
  • 316
    • 0035328312 scopus 로고    scopus 로고
    • Spectra of Anderson type models with decaying randomness
    • M. Krishna, and K. B. Sinha. Spectra of Anderson type models with decaying randomness. Proc. Indian Acad. Sci. Math. Sci., 111(2):179-201, 2001.
    • (2001) Proc. Indian Acad. Sci. Math. Sci , vol.111 , Issue.2 , pp. 179-201
    • Krishna, M.1    Sinha, K.B.2
  • 317
    • 4043100374 scopus 로고    scopus 로고
    • Schrödinger operators with random sparse potentials. Existence of wave operators
    • D. Krutikov. Schrödinger operators with random sparse potentials. Existence of wave operators. Lett. Math. Phys., 67(2):133-139, 2004.
    • (2004) Lett. Math. Phys , vol.67 , Issue.2 , pp. 133-139
    • Krutikov, D.1
  • 318
    • 0036035440 scopus 로고    scopus 로고
    • On the structure of spectra of periodic elliptic operators
    • 537-569 electronic
    • P. Kuchment and S. Levendorskiî. On the structure of spectra of periodic elliptic operators. Trans. Amer. Math. Soc., 354(2):537-569 (electronic), 2002.
    • (2002) Trans. Amer. Math. Soc , vol.354 , Issue.2
    • Kuchment, P.1    Levendorskiî, S.2
  • 319
    • 0001097161 scopus 로고
    • Sur le spectre des opérateur aux différence finies aléatoires
    • H. Kunz and B. Souillard. Sur le spectre des opérateur aux différence finies aléatoires. Commun. Math. Phys., 78:201-246, 1980.
    • (1980) Commun. Math. Phys , vol.78 , pp. 201-246
    • Kunz, H.1    Souillard, B.2
  • 320
    • 37149017222 scopus 로고
    • Répartition d'état d'un opérateur de Schrödinger aléatoire. Distribution empirique des valeurs propres d'une matrice de Jacobi
    • Probability measures on groups, VII Oberwolfach, 1983, of, Springer, Berlin
    • É. le Page. Répartition d'état d'un opérateur de Schrödinger aléatoire. Distribution empirique des valeurs propres d'une matrice de Jacobi. In Probability measures on groups, VII (Oberwolfach, 1983), volume 1064 of Lecture Notes in Math., pages 309-367. Springer, Berlin, 1984.
    • (1984) Lecture Notes in Math , vol.1064 , pp. 309-367
    • le Page, E.1
  • 321
    • 0242329744 scopus 로고    scopus 로고
    • Y. Lee. Burghelea-Friedlander-Kappeler's gluing formula for the zetadeterminant and its applications to the adiabatic decompositions of the zetadeterminant and the analytic torsion. Trans. Amer. Math. Soc, 355(10): 4093-4110 (electronic), 2003.
    • Y. Lee. Burghelea-Friedlander-Kappeler's gluing formula for the zetadeterminant and its applications to the adiabatic decompositions of the zetadeterminant and the analytic torsion. Trans. Amer. Math. Soc, 355(10): 4093-4110 (electronic), 2003.
  • 322
    • 0001043481 scopus 로고
    • Gauge invariance of Schrödinger operators and related spectral properties
    • H. Leinfelder. Gauge invariance of Schrödinger operators and related spectral properties. J. Operator Theory, 9(1):163-179, 1983.
    • (1983) J. Operator Theory , vol.9 , Issue.1 , pp. 163-179
    • Leinfelder, H.1
  • 323
    • 0035981921 scopus 로고    scopus 로고
    • Uniform ergodic theorems on subshifts over a finite alphabet
    • D. Lenz. Uniform ergodic theorems on subshifts over a finite alphabet. Ergodic Theory Dynam. Systems, 22(1):245-255, 2002.
    • (2002) Ergodic Theory Dynam. Systems , vol.22 , Issue.1 , pp. 245-255
    • Lenz, D.1
  • 326
    • 34547141112 scopus 로고    scopus 로고
    • Random Schrödinger operators on manifolds
    • D. Lenz, N. Peyerimhoff, and I. Veselić. Random Schrödinger operators on manifolds. Markov Process. Related Fields, 9(4):717-728, 2003. http://www.arxiv.org/math-ph/0212057.
    • (2003) Markov Process. Related Fields , vol.9 , Issue.4 , pp. 717-728
    • Lenz, D.1    Peyerimhoff, N.2    Veselić, I.3
  • 327
    • 2442701680 scopus 로고    scopus 로고
    • Integrated density of states for random metrics on manifolds
    • D. Lenz, N. Peyerimhoff, and I. Veselić. Integrated density of states for random metrics on manifolds. Proc. London Math. Soc. (3), 88(3):733-752, 2004.
    • (2004) Proc. London Math. Soc. (3) , vol.88 , Issue.3 , pp. 733-752
    • Lenz, D.1    Peyerimhoff, N.2    Veselić, I.3
  • 328
    • 34547175802 scopus 로고    scopus 로고
    • Von Neumann algebras, groupoids and the integrated density of states
    • arXiv.org/abs/math-ph/0203026
    • D. Lenz, N. Peyerimhoff, and I. Veselić. Von Neumann algebras, groupoids and the integrated density of states. Math. Phys. Anal. Geom., 10(1): 1-41, 2007. arXiv.org/abs/math-ph/0203026.
    • (2007) Math. Phys. Anal. Geom , vol.10 , Issue.1 , pp. 1-41
    • Lenz, D.1    Peyerimhoff, N.2    Veselić, I.3
  • 329
    • 34848818794 scopus 로고    scopus 로고
    • Hamiltonians on discrete structures: Jumps of the integrated density of states and uniform convergence
    • Preprint
    • D. Lenz and I. Veselić. Hamiltonians on discrete structures: jumps of the integrated density of states and uniform convergence. Preprint.
    • Lenz, D.1    Veselić, I.2
  • 330
    • 33644951173 scopus 로고    scopus 로고
    • An ergodic theorem for Delone dynamical systems and existence of the density of states
    • D. H. Lenz and P. Stollmann. An ergodic theorem for Delone dynamical systems and existence of the density of states. J. Anal. Math., 97:1-23, 2006. http://www.arxiv.org/math-ph/0310017.
    • (2006) J. Anal. Math , vol.97 , pp. 1-23
    • Lenz, D.H.1    Stollmann, P.2
  • 331
    • 17144383025 scopus 로고    scopus 로고
    • A survey of rigorous results on random Schrödinger operators for amorphous solids
    • H. Leschke, P. Müller, and S. Warzel. A survey of rigorous results on random Schrödinger operators for amorphous solids. Markov Process. Related Fields, 9(4):729-760, 2003. http://www.arXiv.org/cond-mat/0210708).
    • (2003) Markov Process. Related Fields , vol.9 , Issue.4 , pp. 729-760
    • Leschke, H.1    Müller, P.2    Warzel, S.3
  • 332
    • 0000324115 scopus 로고
    • On the parabolic kernel of the Schrödinger operator
    • P. Li and S. Yau. On the parabolic kernel of the Schrödinger operator. Acta Mathematica, 156:153-201, 1986.
    • (1986) Acta Mathematica , vol.156 , pp. 153-201
    • Li, P.1    Yau, S.2
  • 333
    • 84966224507 scopus 로고
    • Bounds on the eigenvalues of the Laplace and Schrödinger operators
    • E. Lieb. Bounds on the eigenvalues of the Laplace and Schrödinger operators. Bull. Amer. Math. Soc., 82(5):751-753, 1976.
    • (1976) Bull. Amer. Math. Soc , vol.82 , Issue.5 , pp. 751-753
    • Lieb, E.1
  • 334
    • 0002624077 scopus 로고
    • Inequalities for the moments of the eigenvalues of the Schrödinger Hamiltonian and their relation to Sobolev inequalities
    • Studies in Math. Phys, Essays in honor of Valentine Bargmann
    • E. Lieb and W. Thirring. Inequalities for the moments of the eigenvalues of the Schrödinger Hamiltonian and their relation to Sobolev inequalities. In Studies in Math. Phys., Essays in honor of Valentine Bargmann, pages 269-303. Princeton Series in Physics, 1976.
    • (1976) Princeton Series in Physics , pp. 269-303
    • Lieb, E.1    Thirring, W.2
  • 335
    • 85009379555 scopus 로고    scopus 로고
    • Lifschitz Memorial Issue. J. Statist. Phys., 38(1-2), 1985.
    • Lifschitz Memorial Issue. J. Statist. Phys., 38(1-2), 1985.
  • 336
    • 85009379559 scopus 로고    scopus 로고
    • I. M. Lifshitz. Structure of the energy spectrum of the impurity bands in disordered solid solutions. Sov. Phys. JETP, 17:1159-1170, 1963. [Russian original: Zh. Eksp. Ter. Fiz. 44: 1723-1741].
    • I. M. Lifshitz. Structure of the energy spectrum of the impurity bands in disordered solid solutions. Sov. Phys. JETP, 17:1159-1170, 1963. [Russian original: Zh. Eksp. Ter. Fiz. 44: 1723-1741].
  • 337
    • 84913893488 scopus 로고
    • The energy spectrum of disordered systems
    • I. M. Lifshitz. The energy spectrum of disordered systems. Adv. Phys., 13:483-536, 1964.
    • (1964) Adv. Phys , vol.13 , pp. 483-536
    • Lifshitz, I.M.1
  • 338
    • 85009379557 scopus 로고    scopus 로고
    • I. M. Lifshitz. Energy spectrum and the quantum states of disordered condensed systems. Sov. Phys. Usp., 7:549-573, 1965. [Russian original: Uspehi Fiz. Nauk 83: 617-663 (1964)].
    • I. M. Lifshitz. Energy spectrum and the quantum states of disordered condensed systems. Sov. Phys. Usp., 7:549-573, 1965. [Russian original: Uspehi Fiz. Nauk 83: 617-663 (1964)].
  • 342
    • 0035646722 scopus 로고    scopus 로고
    • Pointwise theorems for amenable groups
    • E. Lindenstrauss. Pointwise theorems for amenable groups. Invent. Math., 146(2):259-295, 2001.
    • (2001) Invent. Math , vol.146 , Issue.2 , pp. 259-295
    • Lindenstrauss, E.1
  • 343
    • 85009424997 scopus 로고    scopus 로고
    • J. Londergan, C. J.P., and D. Murdock. Binding and scattering in two-dimensional systems, 60 of Lecture Notes in Physics. Springer, 1999.
    • J. Londergan, C. J.P., and D. Murdock. Binding and scattering in two-dimensional systems, volume 60 of Lecture Notes in Physics. Springer, 1999.
  • 344
    • 84972530412 scopus 로고
    • Heat kernels on covering spaces and topological invariants
    • J. Lott. Heat kernels on covering spaces and topological invariants. J. Differential Geom., 35(2):471-510, 1992.
    • (1992) J. Differential Geom , vol.35 , Issue.2 , pp. 471-510
    • Lott, J.1
  • 345
    • 0000445261 scopus 로고
    • 2-invariants by their finite-dimensional analogues
    • 2-invariants by their finite-dimensional analogues. Geom. Funct. Anal., 4(4):455-481, 1994.
    • (1994) Geom. Funct. Anal , vol.4 , Issue.4 , pp. 455-481
    • Lück, W.1
  • 346
    • 4243067988 scopus 로고    scopus 로고
    • 2-invariants: Theory and applications to geometry and K-theory
    • of, Springer-Verlag, Berlin
    • 2-invariants: theory and applications to geometry and K-theory, volume 44 of Ergebnisse der Mathematik und ihrer Grenzgebiete. 3rd Series. Springer-Verlag, Berlin, 2002.
    • (2002) Ergebnisse der Mathematik und ihrer Grenzgebiete. 3rd Series , vol.44
    • Luck, W.1
  • 348
    • 34249923052 scopus 로고
    • Reidemeister torsion and the K-theory of von Neumann algebras
    • W. Lück and M. Rothenberg. Reidemeister torsion and the K-theory of von Neumann algebras. K-Theory, 5(3):213-264, 1991.
    • (1991) K-Theory , vol.5 , Issue.3 , pp. 213-264
    • Lück, W.1    Rothenberg, M.2
  • 349
    • 0040710347 scopus 로고    scopus 로고
    • 2-torsion of hyperbolic manifolds of finite volume
    • 2-torsion of hyperbolic manifolds of finite volume. Geom. Funct. Anal., 9(3):518-567, 1999.
    • (1999) Geom. Funct. Anal , vol.9 , Issue.3 , pp. 518-567
    • Lück, W.1    Schick, T.2
  • 350
    • 34247881029 scopus 로고    scopus 로고
    • 2-signature theorem
    • World Sci. Publishing, River Edge, NJ
    • 2-signature theorem. In High-dimensional manifold topology, pages 362-399. World Sci. Publishing, River Edge, NJ, 2003. http://www.arXiv.org/math.GT/0209161.
    • (2003) High-dimensional manifold topology , pp. 362-399
    • Lück, W.1    Schick, T.2
  • 351
    • 25144492811 scopus 로고    scopus 로고
    • 2-signatures by their compact analogues
    • 2-signatures by their compact analogues. Forum Math., 17(1):31-65, 2005. http://www.arXiv.org/math.GT/0110328.
    • (2005) Forum Math , vol.17 , Issue.1 , pp. 31-65
    • Lück, W.1    Schick, T.2
  • 352
    • 34250100449 scopus 로고
    • Bounds on the density of states of random Schrödinger operators
    • R. S. Maier. Bounds on the density of states of random Schrödinger operators. J. Statist. Phys., 48(3-4):425-447, 1987.
    • (1987) J. Statist. Phys , vol.48 , Issue.3-4 , pp. 425-447
    • Maier, R.S.1
  • 354
  • 355
    • 0002520386 scopus 로고
    • Remark on the absence of absolutely continuous spectrum for d-dimensional Schrödinger operators with random potential for large disorder or low energy
    • F. Martinelli and E. Scoppola. Remark on the absence of absolutely continuous spectrum for d-dimensional Schrödinger operators with random potential for large disorder or low energy. Comm. Math. Phys., 97(3):465-471, 1985.
    • (1985) Comm. Math. Phys , vol.97 , Issue.3 , pp. 465-471
    • Martinelli, F.1    Scoppola, E.2
  • 356
    • 0000097840 scopus 로고
    • 2-analytic torsion
    • 2-analytic torsion. J. Funct. Anal., 107(2):369-386, 1992.
    • (1992) J. Funct. Anal , vol.107 , Issue.2 , pp. 369-386
    • Mathai, V.1
  • 357
    • 0037050305 scopus 로고    scopus 로고
    • Approximating spectral invariants of Harper operators on graphs
    • 111-136, arXiv.org/math.FA/0006138
    • V. Mathai and S. Yates. Approximating spectral invariants of Harper operators on graphs. J. Funct. Anal., 188(1):111-136, 2002. arXiv.org/math.FA/0006138.
    • (2002) J. Funct. Anal , vol.188 , Issue.1
    • Mathai, V.1    Yates, S.2
  • 358
    • 84972572897 scopus 로고
    • On the integrated density of states for the Schrödinger operators with certain random electromagnetic potentials
    • H. Matsumoto. On the integrated density of states for the Schrödinger operators with certain random electromagnetic potentials. J. Math. Soc. Japan, 45(2):197-214, 1993.
    • (1993) J. Math. Soc. Japan , vol.45 , Issue.2 , pp. 197-214
    • Matsumoto, H.1
  • 359
    • 0038174798 scopus 로고    scopus 로고
    • Eigenvalue asymptotics for weakly perturbed Dirac and Schrödinger operators with constant magnetic fields of full rank
    • M. Melgaard and G. Rozenblum. Eigenvalue asymptotics for weakly perturbed Dirac and Schrödinger operators with constant magnetic fields of full rank. Comm. Partial Differential Equations, 28(3-4):697-736, 2003.
    • (2003) Comm. Partial Differential Equations , vol.28 , Issue.3-4 , pp. 697-736
    • Melgaard, M.1    Rozenblum, G.2
  • 361
    • 37149034536 scopus 로고
    • Bounds on the integrated density of electronic states for disordered Hamiltonians
    • G. A. Mezincescu. Bounds on the integrated density of electronic states for disordered Hamiltonians. Phys. Rev. B, 32:6272-6277, 1985.
    • (1985) Phys. Rev. B , vol.32 , pp. 6272-6277
    • Mezincescu, G.A.1
  • 362
    • 26644439227 scopus 로고
    • Internal Lifshitz singularities of disordered finite-difference Schrödinger operators
    • G. A. Mezincescu. Internal Lifshitz singularities of disordered finite-difference Schrödinger operators. Commun. Math. Phys., 103:167-176, 1986.
    • (1986) Commun. Math. Phys , vol.103 , pp. 167-176
    • Mezincescu, G.A.1
  • 363
    • 26644462567 scopus 로고
    • Lifschitz singularities for periodic operators plus random potentials
    • G. A. Mezincescu. Lifschitz singularities for periodic operators plus random potentials. J. Statist. Phys., 49(5-6):1181-1190, 1987.
    • (1987) J. Statist. Phys , vol.49 , Issue.5-6 , pp. 1181-1190
    • Mezincescu, G.A.1
  • 364
    • 21344498311 scopus 로고
    • Internal Lifshitz singularities for one dimensional Schrö dinger operators
    • G. A. Mezincescu. Internal Lifshitz singularities for one dimensional Schrö dinger operators. Commun. Math. Phys., 158:315-325, 1993.
    • (1993) Commun. Math. Phys , vol.158 , pp. 315-325
    • Mezincescu, G.A.1
  • 365
    • 0040068426 scopus 로고
    • Random Schrödinger operators with a constant electric field
    • N. Minami. Random Schrödinger operators with a constant electric field. Ann. Inst. Henri Poincaré, Physique théorique, 56:307-344, 1992.
    • (1992) Ann. Inst. Henri Poincaré, Physique théorique , vol.56 , pp. 307-344
    • Minami, N.1
  • 366
    • 0030553788 scopus 로고    scopus 로고
    • Local fluctuation of the spectrum of a multidimensional Anderson tight binding model
    • N. Minami. Local fluctuation of the spectrum of a multidimensional Anderson tight binding model. Comm. Math. Phys., 177(3):709-725, 1996.
    • (1996) Comm. Math. Phys , vol.177 , Issue.3 , pp. 709-725
    • Minami, N.1
  • 367
    • 17144438142 scopus 로고    scopus 로고
    • Phys. Rev. A (3)
    • 042112, 20
    • K. A. Mitchell. Gauge fields and extrapotentials in constrained quantum systems. Phys. Rev. A (3), 63(4):042112, 20, 2001.
    • (2001) , vol.63 , Issue.4
    • Mitchell, K.A.1
  • 368
    • 5544291378 scopus 로고
    • The local structure of the spectrum of the one-dimensional Schrödinger operator
    • S. A. Molčanov. The local structure of the spectrum of the one-dimensional Schrödinger operator. Comm. Math. Phys., 78(3):429-446, 1980/81.
    • (1980) Comm. Math. Phys , vol.78 , Issue.3 , pp. 429-446
    • Molčanov, S.A.1
  • 369
    • 0002297290 scopus 로고
    • The structure of eigenfunctions of one-dimensional unordered structures
    • S. A. Molčanov. The structure of eigenfunctions of one-dimensional unordered structures. Math. USSR Izvestija, 12:69-101, 1978.
    • (1978) Math. USSR Izvestija , vol.12 , pp. 69-101
    • Molčanov, S.A.1
  • 371
    • 85009365540 scopus 로고    scopus 로고
    • Spectral asymptotics of the Laplaeian on supercritical bond-percolation graphs. http://www.arxiv.org/math-ph/0506053, to appear in
    • P. Müller and P, Stollmann. Spectral asymptotics of the Laplaeian on supercritical bond-percolation graphs. http://www.arxiv.org/math-ph/0506053, to appear in J. Funct, Anal.
    • J. Funct, Anal
    • Müller, P.1    Stollmann, P.2
  • 372
    • 0033235583 scopus 로고    scopus 로고
    • Spectral shift function for trapping energies in the semiclassical limit
    • S. Nakamura. Spectral shift function for trapping energies in the semiclassical limit, Comm. Math. Phys., 208(1):173-193, 1999.
    • (1999) Comm. Math. Phys , vol.208 , Issue.1 , pp. 173-193
    • Nakamura, S.1
  • 373
    • 0034346385 scopus 로고    scopus 로고
    • Lifshitz tail for 2D discrete Schrödinger operator with random magnetic field
    • S. Nakamura, Lifshitz tail for 2D discrete Schrödinger operator with random magnetic field, Ann. Henri Poincaré, 1(5):823-835, 2000.
    • (2000) Ann. Henri Poincaré , vol.1 , Issue.5 , pp. 823-835
    • Nakamura, S.1
  • 374
    • 0034343124 scopus 로고    scopus 로고
    • Lifshitz tail for Schrödinger operator with random magnetic field
    • S. Nakamura, Lifshitz tail for Schrödinger operator with random magnetic field, Comm. Math. Phys., 214(3):565-572, 2000.
    • (2000) Comm. Math. Phys , vol.214 , Issue.3 , pp. 565-572
    • Nakamura, S.1
  • 375
    • 0003035749 scopus 로고    scopus 로고
    • A remark on the Dirichlet-Neumann decoupling and the integrated density of states
    • S. Nakamura. A remark on the Dirichlet-Neumann decoupling and the integrated density of states, J. Funct. Anal., 179:136-152, 2001.
    • (2001) J. Funct. Anal , vol.179 , pp. 136-152
    • Nakamura, S.1
  • 376
    • 0036475756 scopus 로고    scopus 로고
    • A remark on the Lifshitz tail for Schrödinger operator with random magnetic field
    • S. Nakamura, A remark on the Lifshitz tail for Schrödinger operator with random magnetic field, Proc. Indian Acad. Sci. Math. Sci., 112(1): 183-187, 2002.
    • (2002) Proc. Indian Acad. Sci. Math. Sci , vol.112 , Issue.1 , pp. 183-187
    • Nakamura, S.1
  • 377
    • 12844278812 scopus 로고    scopus 로고
    • Calculation of the Hall conductivity by Abel limit
    • F. Nakano, Calculation of the Hall conductivity by Abel limit, Ann. Inst. H. Poincaré Phys. Théor., 69(4):441-455, 1998.
    • (1998) Ann. Inst. H. Poincaré Phys. Théor , vol.69 , Issue.4 , pp. 441-455
    • Nakano, F.1
  • 378
    • 33747713923 scopus 로고    scopus 로고
    • The repulsion between localization centers in the Anderson model
    • F. Nakano, The repulsion between localization centers in the Anderson model. J. Stat. Phys., 123(4):803-810, 2006, http://arxiv.org/abs/math- ph/0603029.
    • (2006) J. Stat. Phys , vol.123 , Issue.4 , pp. 803-810
    • Nakano, F.1
  • 379
    • 0000188166 scopus 로고
    • On the spectral distribution of the Schrödinger operator with random potential
    • S. Nakao, On the spectral distribution of the Schrödinger operator with random potential, Japan. J. Math. (N.S.), 3(1):111-139, 1977.
    • (1977) Japan. J. Math. (N.S.) , vol.3 , Issue.1 , pp. 111-139
    • Nakao, S.1
  • 380
    • 0000922186 scopus 로고
    • Morse inequalities and von Neumann invariants of non-simply connected manifolds
    • In Russian
    • S. P. Novikov and M. A. Shubin. Morse inequalities and von Neumann invariants of non-simply connected manifolds, Uspekhi Matem. Nauk, 41(5):222, 1986, (In Russian).
    • (1986) Uspekhi Matem. Nauk , vol.41 , Issue.5 , pp. 222
    • Novikov, S.P.1    Shubin, M.A.2
  • 382
    • 34248513005 scopus 로고    scopus 로고
    • The secondary Novikov-Shubin invariants of groups and quasiisometry
    • S.-I. Oguni. The secondary Novikov-Shubin invariants of groups and quasiisometry. J. Math. Soc. Japan, 59(1):223-237, 2007, http://www.math.kyoto-u.ac.jp/preprint/preprint2005.html.
    • (2007) J. Math. Soc. Japan , vol.59 , Issue.1 , pp. 223-237
    • Oguni, S.-I.1
  • 383
    • 0002991617 scopus 로고
    • The Shannon-McMillan-Breiman theorem for a class of amenable groups
    • D. Ornstein and B. Weiss, The Shannon-McMillan-Breiman theorem for a class of amenable groups. Israel J. Math., 44(1):53-60, 1983.
    • (1983) Israel J. Math , vol.44 , Issue.1 , pp. 53-60
    • Ornstein, D.1    Weiss, B.2
  • 384
    • 0141805331 scopus 로고
    • Selfaverageability of the number of states of the Schrödinger equation with a random potential
    • Vyp, 2
    • L. A. Pastur. Selfaverageability of the number of states of the Schrödinger equation with a random potential, Mat. Fiz. i Funkcional. Anal., (Vyp, 2):111-116, 238, 1971.
    • (1971) Mat. Fiz. i Funkcional. Anal , vol.111-116 , pp. 238
    • Pastur, L.A.1
  • 385
    • 34250456068 scopus 로고
    • On the distribution of the eigenvalues of the Schrödinger equation with a random potential
    • L. A. Pastur. On the distribution of the eigenvalues of the Schrödinger equation with a random potential, Funct. Anal. Appl, 8:163-165, 1972.
    • (1972) Funct. Anal. Appl , vol.8 , pp. 163-165
    • Pastur, L.A.1
  • 386
    • 34547230574 scopus 로고
    • The distribution of the eigenvalues of Schrödinger's equation with a random potential
    • 158, Akad. Nauk Ukrain, SSR, Fiz.-Tehn. Inst. Nizkih Temperatur, Kharkov
    • L. A. Pastur, The distribution of the eigenvalues of Schrödinger's equation with a random potential, In Mathematical physics and functional analysis, No. V (Russian), pages 141-143, 158, Akad. Nauk Ukrain, SSR, Fiz.-Tehn. Inst. Nizkih Temperatur, Kharkov, 1974.
    • (1974) Mathematical physics and functional analysis, No. V (Russian) , pp. 141-143
    • Pastur, L.A.1
  • 387
    • 0002859104 scopus 로고
    • Behaviour of some Wiener integrals as t → ∞ and the density of states of the Schrödinger equation with a random potential
    • L. A. Pastur, Behaviour of some Wiener integrals as t → ∞ and the density of states of the Schrödinger equation with a random potential, Teor. Mat. Fiz., 32:88-95, 1977.
    • (1977) Teor. Mat. Fiz , vol.32 , pp. 88-95
    • Pastur, L.A.1
  • 388
    • 34250250635 scopus 로고
    • Spectral properties of disordered systems in the one-body approximation
    • L. A. Pastur, Spectral properties of disordered systems in the one-body approximation. Commun. Math. Phys., 75:179-196, 1980.
    • (1980) Commun. Math. Phys , vol.75 , pp. 179-196
    • Pastur, L.A.1
  • 390
    • 0003288575 scopus 로고
    • Amenability
    • of, American Mathematical Society, Providence, RI
    • A. L. T. Paterson. Amenability, volume 29 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 1988.
    • (1988) Mathematical Surveys and Monographs , vol.29
    • Paterson, A.L.T.1
  • 391
    • 0038968342 scopus 로고
    • Hankel operators in the perturbation theory of unbounded self-adjoint operators
    • Analysis and partial differential equations, of, Dekker, New York
    • V. V. Peller. Hankel operators in the perturbation theory of unbounded self-adjoint operators. In Analysis and partial differential equations, volume 122 of Lecture Notes in Pure and Appl. Math., pages 529-544. Dekker, New York, 1990.
    • (1990) Lecture Notes in Pure and Appl. Math , vol.122 , pp. 529-544
    • Peller, V.V.1
  • 392
    • 0141676303 scopus 로고    scopus 로고
    • Integrated density of states for ergodic random Schrödinger operators on manifolds
    • N. Peyerimhoff and I. Veselić. Integrated density of states for ergodic random Schrödinger operators on manifolds. Geom. Dedicata, 91(1):117-135, 2002.
    • (2002) Geom. Dedicata , vol.91 , Issue.1 , pp. 117-135
    • Peyerimhoff, N.1    Veselić, I.2
  • 393
    • 85009419589 scopus 로고    scopus 로고
    • O. Post. Periodic Manifolds, Spectral Gaps, and Eigenvalues in Gaps. Doctoral thesis, Technische Universität Braunschweig, D-38092 Braunschweig, July 2000. http://www.iram.rwth-aachen.de/post/index.html.
    • O. Post. Periodic Manifolds, Spectral Gaps, and Eigenvalues in Gaps. Doctoral thesis, Technische Universität Braunschweig, D-38092 Braunschweig, July 2000. http://www.iram.rwth-aachen.de/"post/index.html.
  • 394
    • 0037219901 scopus 로고    scopus 로고
    • Periodic manifolds with spectral gaps
    • O. Post. Periodic manifolds with spectral gaps. J. Differential Equations, 187(1):23-45, 2003.
    • (2003) J. Differential Equations , vol.187 , Issue.1 , pp. 23-45
    • Post, O.1
  • 395
    • 0031530859 scopus 로고    scopus 로고
    • Infinite degeneracy for a Landau Hamiltonian with Poisson impurities
    • J. V. Pulé and M. Scrowston. Infinite degeneracy for a Landau Hamiltonian with Poisson impurities. J. Math. Phys., 38(12):6304-6314, 1997.
    • (1997) J. Math. Phys , vol.38 , Issue.12 , pp. 6304-6314
    • Pulé, J.V.1    Scrowston, M.2
  • 396
    • 0034347357 scopus 로고    scopus 로고
    • The spectrum of a magnetic Schrödinger operator with randomly located delta impurities
    • J. V. Pulé and M. Scrowston. The spectrum of a magnetic Schrödinger operator with randomly located delta impurities. J. Math. Phys., 41(5):2805-2825, 2000.
    • (2000) J. Math. Phys , vol.41 , Issue.5 , pp. 2805-2825
    • Pulé, J.V.1    Scrowston, M.2
  • 397
    • 85009395979 scopus 로고    scopus 로고
    • A. B. Pushnitskiǐ. A representation for the spectral shift function in the case of perturbations of fixed sign. Algebra i Analiz, 9(6):197-213, 1997. [English translation in St. Petersburg Math. J. 9(6):1181-1194, 1998].
    • A. B. Pushnitskiǐ. A representation for the spectral shift function in the case of perturbations of fixed sign. Algebra i Analiz, 9(6):197-213, 1997. [English translation in St. Petersburg Math. J. 9(6):1181-1194, 1998].
  • 398
    • 85009395980 scopus 로고    scopus 로고
    • A. B. Pushnitskiǐ. Integral estimates for the spectral shift function. Algebra i Analiz, 10(6):198-233, 1998. [English translation in St. Petersburg Math. J. 10 (6): 1047-1070, 1999],
    • A. B. Pushnitskiǐ. Integral estimates for the spectral shift function. Algebra i Analiz, 10(6):198-233, 1998. [English translation in St. Petersburg Math. J. 10 (6): 1047-1070, 1999],
  • 399
    • 0033240087 scopus 로고    scopus 로고
    • Estimates for the spectral shift function of the polyharmonic operator
    • A. B. Pushnitskiǐ. Estimates for the spectral shift function of the polyharmonic operator. J. Math. Phys., 40(11):5578-5592, 1999.
    • (1999) J. Math. Phys , vol.40 , Issue.11 , pp. 5578-5592
    • Pushnitskiǐ, A.B.1
  • 400
    • 0010568693 scopus 로고    scopus 로고
    • Spectral shift function of the Schrödinger operator in the large coupling constant limit
    • A. B. Pushnitskiǐ. Spectral shift function of the Schrödinger operator in the large coupling constant limit. Comm. Partial Differential Equations, 25(3-4): 703-736, 2000.
    • (2000) Comm. Partial Differential Equations , vol.25 , Issue.3-4 , pp. 703-736
    • Pushnitskiǐ, A.B.1
  • 401
    • 0036383360 scopus 로고    scopus 로고
    • Spectral shift function of the Schrödinger operator in the large coupling constant limit. II. Positive perturbations
    • A. B. Pushnitskiǐ and M. Ruzhansky. Spectral shift function of the Schrödinger operator in the large coupling constant limit. II. Positive perturbations. Comm. Partial Differential Equations, 27(7-8):1373-1405, 2002.
    • (2002) Comm. Partial Differential Equations , vol.27 , Issue.7-8 , pp. 1373-1405
    • Pushnitskiǐ, A.B.1    Ruzhansky, M.2
  • 402
    • 34247178455 scopus 로고    scopus 로고
    • Spectral shift function for Schrödinger operators in constant magnetic fields
    • G. Raikov. Spectral shift function for Schrödinger operators in constant magnetic fields. Cubo, 7(2): 171-199, 2005.
    • (2005) Cubo , vol.7 , Issue.2 , pp. 171-199
    • Raikov, G.1
  • 403
    • 33749047097 scopus 로고    scopus 로고
    • Spectral shift function for magnetic Schrödinger operators
    • Mathematical physics of quantum mechanics, of, Springer, Berlin
    • G. Raikov. Spectral shift function for magnetic Schrödinger operators. In Mathematical physics of quantum mechanics, volume 690 of Lecture Notes in Phys., pages 451-465. Springer, Berlin, 2006.
    • (2006) Lecture Notes in Phys , vol.690 , pp. 451-465
    • Raikov, G.1
  • 404
    • 85009370130 scopus 로고    scopus 로고
    • G. D. Raikov. The integrated density of states for a random Schrödinger operator in strong magnetic fields. II. Asymptotics near higher Landau levels. In Partial differential equations and spectral theory (Clausthal, 2000), 126 of Oper. Theory Adv. Appl., pages 281-292. Birkhäuser, Basel, 2001.
    • G. D. Raikov. The integrated density of states for a random Schrödinger operator in strong magnetic fields. II. Asymptotics near higher Landau levels. In Partial differential equations and spectral theory (Clausthal, 2000), volume 126 of Oper. Theory Adv. Appl., pages 281-292. Birkhäuser, Basel, 2001.
  • 405
    • 0036815423 scopus 로고    scopus 로고
    • Quasi-classical versus non-classical spectral asymptotics for magnetic Schrödinger operators with decreasing electric potentials
    • G. D. Raikov and S. Warzel. Quasi-classical versus non-classical spectral asymptotics for magnetic Schrödinger operators with decreasing electric potentials. Rev. Math. Phys., 14(10):1051-1072, 2002.
    • (2002) Rev. Math. Phys , vol.14 , Issue.10 , pp. 1051-1072
    • Raikov, G.D.1    Warzel, S.2
  • 406
    • 0000119424 scopus 로고
    • R-torsion and the Laplaeian on Riemannian manifolds
    • D. B. Ray and I. M. Singer. R-torsion and the Laplaeian on Riemannian manifolds. Advances in Math., 7:145-210, 1971.
    • (1971) Advances in Math , vol.7 , pp. 145-210
    • Ray, D.B.1    Singer, I.M.2
  • 412
    • 37149029872 scopus 로고
    • The central limit theorem for the spectrum of random Jacobi matrices
    • A. Režnikova. The central limit theorem for the spectrum of random Jacobi matrices. Theory Probab. Appl., 25:504-513, 1981.
    • (1981) Theory Probab. Appl , vol.25 , pp. 504-513
    • Režnikova, A.1
  • 413
    • 34250247203 scopus 로고
    • The central limit theorem for the spectrum of the random one-dimensional Schrdinger operator
    • A. Režnikova. The central limit theorem for the spectrum of the random one-dimensional Schrdinger operator. J. Stat. Phys., 25:291-308, 1981.
    • (1981) J. Stat. Phys , vol.25 , pp. 291-308
    • Režnikova, A.1
  • 415
    • 37149034229 scopus 로고
    • Étude des opérateurs de Schrödinger à, potentiel aléatoire en dimension 1
    • G. Royer. Étude des opérateurs de Schrödinger à, potentiel aléatoire en dimension 1. Bull. Soc. Math. France, 110(1):27-48, 1982.
    • (1982) Bull. Soc. Math. France , vol.110 , Issue.1 , pp. 27-48
    • Royer, G.1
  • 416
    • 0000424726 scopus 로고
    • Distribution of the discrete spectrum of singular differential operators
    • G. V. Rozenbljum. Distribution of the discrete spectrum of singular differential operators. Dokl Akad. Nauk SSSR, 202:1012-1015, 1972.
    • (1972) Dokl Akad. Nauk SSSR , vol.202 , pp. 1012-1015
    • Rozenbljum, G.V.1
  • 418
    • 0010567786 scopus 로고    scopus 로고
    • Spectral shift function in the large coupling constant limit
    • O. Safronov. Spectral shift function in the large coupling constant limit. J. Funct. Anal., 182(1):151-169, 2001.
    • (2001) J. Funct. Anal , vol.182 , Issue.1 , pp. 151-169
    • Safronov, O.1
  • 419
    • 0011159603 scopus 로고    scopus 로고
    • The creation of spectral gaps by graph decoration
    • J. H. Schenker and M. Aizenman. The creation of spectral gaps by graph decoration. Lett. Math. Phys., 53(3):253-262, 2000.
    • (2000) Lett. Math. Phys , vol.53 , Issue.3 , pp. 253-262
    • Schenker, J.H.1    Aizenman, M.2
  • 420
    • 0034422251 scopus 로고    scopus 로고
    • 2-Betti numbers
    • 2-Betti numbers. Math. Ann., 317(4):727-750, 2000.
    • (2000) Math. Ann , vol.317 , Issue.4 , pp. 727-750
    • Schick, T.1
  • 421
    • 23044528276 scopus 로고    scopus 로고
    • 2-Betti numbers. Trans. Amer. Math. Soc., 353(8):3247-3265 (electronic), 2001.
    • 2-Betti numbers. Trans. Amer. Math. Soc., 353(8):3247-3265 (electronic), 2001.
  • 422
    • 0039838501 scopus 로고    scopus 로고
    • 2-index theorem for elliptic differential boundary problems
    • 2-index theorem for elliptic differential boundary problems. Pacific J. Math., 197(2):423-439, 2001.
    • (2001) Pacific J. Math , vol.197 , Issue.2 , pp. 423-439
    • Schick, T.1
  • 423
    • 0036934624 scopus 로고    scopus 로고
    • Frequency concentration and localization lengths for the Anderson model at small disorders
    • Dedicated to the memory of Tom Wolff
    • W. Schlag, C. Shubin, and T. Wolff. Frequency concentration and localization lengths for the Anderson model at small disorders. J. Anal Math., 88:173-220, 2002. Dedicated to the memory of Tom Wolff.
    • (2002) J. Anal Math , vol.88 , pp. 173-220
    • Schlag, W.1    Shubin, C.2    Wolff, T.3
  • 424
    • 7444256558 scopus 로고    scopus 로고
    • Perturbation theory for Lyapunov exponents of an Anderson model on a strip
    • H. Schulz-Baldes. Perturbation theory for Lyapunov exponents of an Anderson model on a strip. Geom. Funct. Anal., 14(5):1089-1117, 2004.
    • (2004) Geom. Funct. Anal , vol.14 , Issue.5 , pp. 1089-1117
    • Schulz-Baldes, H.1
  • 425
    • 0034695295 scopus 로고    scopus 로고
    • Simultaneous quantization of edge and bulk Hall conductivity
    • H. Schulz-Baldes, J. Kellendonk, and T. Richter. Simultaneous quantization of edge and bulk Hall conductivity. J. Phys. A, 33(2):L27-L32, 2000.
    • (2000) J. Phys. A , vol.33 , Issue.2
    • Schulz-Baldes, H.1    Kellendonk, J.2    Richter, T.3
  • 426
    • 8744309710 scopus 로고
    • Localization and quantum percolation
    • Y. Shapir, A. Aharony, and A. B. Harris. Localization and quantum percolation. Phys. Rev. Lett., 49(7):486-489, 1982.
    • (1982) Phys. Rev. Lett , vol.49 , Issue.7 , pp. 486-489
    • Shapir, Y.1    Aharony, A.2    Harris, A.B.3
  • 427
    • 0037143999 scopus 로고    scopus 로고
    • The periodic Schrödinger operators with potentials in the Morrey class
    • Z. Shen. The periodic Schrödinger operators with potentials in the Morrey class. J. Funct. Anal., 193(2):314-345, 2002.
    • (2002) J. Funct. Anal , vol.193 , Issue.2 , pp. 314-345
    • Shen, Z.1
  • 428
    • 0348056516 scopus 로고    scopus 로고
    • Absolute continuity of the spectrum of the two-dimensional periodic Schrödinger operator with a positive electric potential
    • R. G. Shterenberg. Absolute continuity of the spectrum of the two-dimensional periodic Schrödinger operator with a positive electric potential. Algebra i Analiz, 13(4):196-228, 2001.
    • (2001) Algebra i Analiz , vol.13 , Issue.4 , pp. 196-228
    • Shterenberg, R.G.1
  • 429
    • 0032221790 scopus 로고    scopus 로고
    • Some harmonic analysis questions suggested by Anderson-Bernoulli models
    • C. Shubin, R. Vakilian, and T. Wolff. Some harmonic analysis questions suggested by Anderson-Bernoulli models. Geom. Funct. Anal., 8(5):932-964, 1998.
    • (1998) Geom. Funct. Anal , vol.8 , Issue.5 , pp. 932-964
    • Shubin, C.1    Vakilian, R.2    Wolff, T.3
  • 430
    • 85009429173 scopus 로고    scopus 로고
    • M. A. Shubin. The density of states for elliptic operators with almost periodic coefficients. Godišnik Visš. UČebn. Zaved. Priložna Mat., 11(2):209-216 (1977), 1975. Conference on Differential Equations and Applications (Ruse, 1975).
    • M. A. Shubin. The density of states for elliptic operators with almost periodic coefficients. Godišnik Visš. UČebn. Zaved. Priložna Mat., 11(2):209-216 (1977), 1975. Conference on Differential Equations and Applications (Ruse, 1975).
  • 431
    • 85009419584 scopus 로고    scopus 로고
    • M. A. Shubin. Spectral theory and the index of elliptic operators with almostperiodic coefficients. Uspekhi Mat. Nauk, 34(2(206)):95-135, 1979. [English translation: Russ. Math. Surveys, 34:109-157, 1979].
    • M. A. Shubin. Spectral theory and the index of elliptic operators with almostperiodic coefficients. Uspekhi Mat. Nauk, 34(2(206)):95-135, 1979. [English translation: Russ. Math. Surveys, 34:109-157, 1979].
  • 432
    • 0001183671 scopus 로고
    • Density of states of self adjoint operators with almost periodic coefficients
    • M. A. Shubin. Density of states of self adjoint operators with almost periodic coefficients. Amer. Math. Soc. Translations, 118:307-339, 1982.
    • (1982) Amer. Math. Soc. Translations , vol.118 , pp. 307-339
    • Shubin, M.A.1
  • 433
    • 0030304014 scopus 로고    scopus 로고
    • Semiclassical asymptotics on covering manifolds and Morse inequalities
    • M. A. Shubin. Semiclassical asymptotics on covering manifolds and Morse inequalities. Geom. Funct. Anal., 6(2):370-409, 1996.
    • (1996) Geom. Funct. Anal , vol.6 , Issue.2 , pp. 370-409
    • Shubin, M.A.1
  • 434
    • 2442703637 scopus 로고
    • Maximal ergodic theorems on groups
    • A. Shulman. Maximal ergodic theorems on groups. Dep. Lit. NIINTI, 2184, 1988.
    • (1988) Dep. Lit. NIINTI , vol.2184
    • Shulman, A.1
  • 435
    • 0039740412 scopus 로고
    • Classical boundary conditions as a technical tool in modern mathematical physics
    • B. Simon. Classical boundary conditions as a technical tool in modern mathematical physics. Adv. in Math., 30(3):268-281, 1978.
    • (1978) Adv. in Math , vol.30 , Issue.3 , pp. 268-281
    • Simon, B.1
  • 436
    • 0010711876 scopus 로고
    • Functional integration and quantum physics
    • of, Academic Press Inc, Harcourt Brace Jovanovich Publishers, New York
    • B. Simon. Functional integration and quantum physics, volume 86 of Pure and Applied Mathematics. Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York, 1979.
    • (1979) Pure and Applied Mathematics , vol.86
    • Simon, B.1
  • 437
    • 0003335754 scopus 로고
    • Trace Ideals and their Applications
    • Cambridge University Press, Cambridge
    • B. Simon. Trace Ideals and their Applications. London Mathematical Society Lecture Note Series. 35. Cambridge University Press, Cambridge, 1979.
    • (1979) London Mathematical Society Lecture Note Series , vol.35
    • Simon, B.1
  • 438
    • 0001471315 scopus 로고
    • Almost periodic Schrödinger operators: A review
    • B. Simon. Almost periodic Schrödinger operators: a review. Adv. in Appl. Math., 3(4):463-490, 1982.
    • (1982) Adv. in Appl. Math , vol.3 , Issue.4 , pp. 463-490
    • Simon, B.1
  • 439
    • 85016600983 scopus 로고
    • Schrödinger semigroups
    • B. Simon. Schrödinger semigroups. Bull. Am. Math. Soc., 7:447-526, 1982.
    • (1982) Bull. Am. Math. Soc , vol.7 , pp. 447-526
    • Simon, B.1
  • 440
    • 0002961358 scopus 로고
    • Lifschitz tails for the Anderson model
    • B. Simon. Lifschitz tails for the Anderson model. J. Stat. Phys., 38:65-76, 1985.
    • (1985) J. Stat. Phys , vol.38 , pp. 65-76
    • Simon, B.1
  • 441
    • 0009283963 scopus 로고
    • Internal Lifschitz tails
    • B. Simon. Internal Lifschitz tails. J. Statist. Phys., 46(5-6):911-918, 1987.
    • (1987) J. Statist. Phys , vol.46 , Issue.5-6 , pp. 911-918
    • Simon, B.1
  • 442
    • 85009365535 scopus 로고    scopus 로고
    • B. Simon. Cyclic vectors in the Anderson model. Rev. Math. Phys., 6(5A): 1183-1185, 1994. Special issue dedicated to Elliott H. Lieb.
    • B. Simon. Cyclic vectors in the Anderson model. Rev. Math. Phys., 6(5A): 1183-1185, 1994. Special issue dedicated to Elliott H. Lieb.
  • 443
    • 85009370123 scopus 로고    scopus 로고
    • B. Simon. Spectral analysis of rank one perturbations and applications. In L. R. J. Feldman, R. Froese, editor, Mathematical quantum theory. II. Schrödinger operators (Vancouver, 1993), 8 of CRM Proc. Lecture Notes 8, pages 109-149. Amer. Math. Soc., Providence, RI, 1995.
    • B. Simon. Spectral analysis of rank one perturbations and applications. In L. R. J. Feldman, R. Froese, editor, Mathematical quantum theory. II. Schrödinger operators (Vancouver, 1993), volume 8 of CRM Proc. Lecture Notes Vol. 8, pages 109-149. Amer. Math. Soc., Providence, RI, 1995.
  • 444
    • 84990576488 scopus 로고
    • Singular continuous spectrum under rank one perturbations and localization for random Hamiltonians
    • B. Simon and T. Wolff. Singular continuous spectrum under rank one perturbations and localization for random Hamiltonians. Comm. Pure Appl. Math., 39:75-90, 1986.
    • (1986) Comm. Pure Appl. Math , vol.39 , pp. 75-90
    • Simon, B.1    Wolff, T.2
  • 445
    • 0034349737 scopus 로고    scopus 로고
    • Localization in one dimensional random media: A scattering theoretic approach
    • R. Sims and G. Stolz. Localization in one dimensional random media: a scattering theoretic approach. Comm. Math. Phys., 213(3):575-597, 2000.
    • (2000) Comm. Math. Phys , vol.213 , Issue.3 , pp. 575-597
    • Sims, R.1    Stolz, G.2
  • 446
    • 84934822075 scopus 로고
    • Structure of the spectrum of the multidimensional Schrödinger operator with a periodic potential
    • M. M. Skriganov. Structure of the spectrum of the multidimensional Schrödinger operator with a periodic potential. Dokl. Akad. Nauk. SSSR, 262:846-850, 1984.
    • (1984) Dokl. Akad. Nauk. SSSR , vol.262 , pp. 846-850
    • Skriganov, M.M.1
  • 447
    • 2842566103 scopus 로고
    • The spectrum band structure of the three-dimensional Schrödinger operator with periodic potential
    • M. M. Skriganov. The spectrum band structure of the three-dimensional Schrödinger operator with periodic potential. Invent. Math., 80(1):107-121, 1985.
    • (1985) Invent. Math , vol.80 , Issue.1 , pp. 107-121
    • Skriganov, M.M.1
  • 448
    • 85009401121 scopus 로고    scopus 로고
    • M. M. Skriganov. Geometric and arithmetric methods in the spectral theory of multidimensional periodic operators. Proc. of the Stecklov Institute of Mathematics, 2:vi+121 pp., 1987.
    • M. M. Skriganov. Geometric and arithmetric methods in the spectral theory of multidimensional periodic operators. Proc. of the Stecklov Institute of Mathematics, 2:vi+121 pp., 1987.
  • 449
    • 0001837689 scopus 로고
    • Efficient bounds for the spectral shift function
    • A. Sobolev. Efficient bounds for the spectral shift function. Ann. Inst. Henri, Poincaré, 58:55-83, 1993.
    • (1993) Ann. Inst. Henri, Poincaré , vol.58 , pp. 55-83
    • Sobolev, A.1
  • 450
    • 0033242631 scopus 로고    scopus 로고
    • Absolute continuity of the periodic magnetic Schrödinger operator
    • A. V. Sobolev. Absolute continuity of the periodic magnetic Schrödinger operator. Invent. Math., 137(1):85-112, 1999.
    • (1999) Invent. Math , vol.137 , Issue.1 , pp. 85-112
    • Sobolev, A.V.1
  • 452
    • 0040884033 scopus 로고
    • The Schrödinger equation with a random potential - a mathematical review
    • K. Osterwaler and R. Stora, editors, Amsterdam, North-Holland
    • T. Spencer. The Schrödinger equation with a random potential - a mathematical review. In K. Osterwaler and R. Stora, editors, Phénomènes critiques, systèmes aléatoires, théories de jauge, Part I, II (Les Houches, 1984), pages 895-944, Amsterdam, 1986. North-Holland.
    • (1986) Phénomènes critiques, systèmes aléatoires, théories de jauge, Part I, II (Les Houches, 1984) , pp. 895-944
    • Spencer, T.1
  • 453
    • 0000083362 scopus 로고
    • Localization for random and almost-periodic potentials
    • T. Spencer. Localization for random and almost-periodic potentials. J. Stat. Phys., 51:1009-1017, 1988.
    • (1988) J. Stat. Phys , vol.51 , pp. 1009-1017
    • Spencer, T.1
  • 455
    • 51249169947 scopus 로고
    • A convergence theorem for Dirichlet forms with applications to boundary value problems with varying domains
    • P. Stollmann. A convergence theorem for Dirichlet forms with applications to boundary value problems with varying domains. Math. Z., 219:275-287, 1995.
    • (1995) Math. Z , vol.219 , pp. 275-287
    • Stollmann, P.1
  • 456
    • 0012377510 scopus 로고    scopus 로고
    • Lifshitz asymptotics via linear coupling of disorder
    • P. Stollmann. Lifshitz asymptotics via linear coupling of disorder. Math. Phys. Anal. Geom., 2(3):279-289, 1999.
    • (1999) Math. Phys. Anal. Geom , vol.2 , Issue.3 , pp. 279-289
    • Stollmann, P.1
  • 457
    • 0034344396 scopus 로고    scopus 로고
    • Wegner estimates and localization for continuum Anderson models with some singular distributions
    • P. Stollmann. Wegner estimates and localization for continuum Anderson models with some singular distributions. Arch. Math. (Basel), 75(4):307-311, 2000.
    • (2000) Arch. Math. (Basel) , vol.75 , Issue.4 , pp. 307-311
    • Stollmann, P.1
  • 458
    • 0003203493 scopus 로고    scopus 로고
    • Caught by disorder: Bound States in Random Media
    • of, Birkhäuser
    • P. Stollmann. Caught by disorder: Bound States in Random Media, volume 20 of Progress in Mathematical Physics. Birkhäuser, 2001.
    • (2001) Progress in Mathematical Physics , vol.20
    • Stollmann, P.1
  • 459
    • 0034239191 scopus 로고    scopus 로고
    • Non-monotonic random Schrödinger operators: The Anderson model
    • G. Stolz. Non-monotonic random Schrödinger operators: the Anderson model. J. Math. Anal. Appl., 248(1):173-183, 2000.
    • (2000) J. Math. Anal. Appl , vol.248 , Issue.1 , pp. 173-183
    • Stolz, G.1
  • 460
    • 0036475311 scopus 로고    scopus 로고
    • Strategies in localization proofs for one-dimensional random Schrödinger operators
    • 229-243, Spectral and inverse spectral theory Goa
    • G. Stolz. Strategies in localization proofs for one-dimensional random Schrödinger operators. Proc. Indian Acad. Sci. Math. Sci., 112(1):229-243, 2002. Spectral and inverse spectral theory (Goa, 2000).
    • (2000) Proc. Indian Acad. Sci. Math. Sci , vol.112 , Issue.1
    • Stolz, G.1
  • 462
    • 34250207806 scopus 로고
    • A periodic Schrödinger operator on an abelian cover
    • T. Sunada. A periodic Schrödinger operator on an abelian cover. J. Fac Sci. Univ. Tokyo Sect. IA Math., 37(3):575-583, 1990.
    • (1990) J. Fac Sci. Univ. Tokyo Sect. IA Math , vol.37 , Issue.3 , pp. 575-583
    • Sunada, T.1
  • 463
    • 0001056852 scopus 로고
    • Group C* -algebras and the spectrum of a periodic Schrödinger operator on a manifold
    • T. Sunada. Group C* -algebras and the spectrum of a periodic Schrödinger operator on a manifold. Canad. J. Math., 44(1):180-193, 1992.
    • (1992) Canad. J. Math , vol.44 , Issue.1 , pp. 180-193
    • Sunada, T.1
  • 464
    • 84990582138 scopus 로고
    • Lifschitz tail and Wiener sausage on hyperbolic space
    • A.-S. Sznitman. Lifschitz tail and Wiener sausage on hyperbolic space. Comm. Pure Appl. Math., 42(8):1033-1065, 1989.
    • (1989) Comm. Pure Appl. Math , vol.42 , Issue.8 , pp. 1033-1065
    • Sznitman, A.-S.1
  • 465
    • 0001500492 scopus 로고
    • Lifschitz tail and Wiener sausage. I, II
    • A.-S. Sznitman. Lifschitz tail and Wiener sausage. I, II. J. Funct. Anal., 94(2):223-246, 247-272, 1990.
    • (1990) J. Funct. Anal , vol.94 , Issue.2
    • Sznitman, A.-S.1
  • 466
    • 84990627117 scopus 로고
    • Lifschitz tail on hyperbolic space: Neumann conditions
    • A.-S. Sznitman. Lifschitz tail on hyperbolic space: Neumann conditions. Comm. Pure Appl. Math., 43(1): 1-30, 1990.
    • (1990) Comm. Pure Appl. Math , vol.43 , Issue.1 , pp. 1-30
    • Sznitman, A.-S.1
  • 469
    • 0000504466 scopus 로고
    • Ergodic theorems for general dynamical systems
    • A. A. Tempelman. Ergodic theorems for general dynamical systems. Dokl. Akad. Nauk SSSR, 176:790-793, 1967.
    • (1967) Dokl. Akad. Nauk SSSR , vol.176 , pp. 790-793
    • Tempelman, A.A.1
  • 470
    • 0002613757 scopus 로고
    • Ergodic theorems for general dynamical sytems
    • A. A. Tempelman. Ergodic theorems for general dynamical sytems. Trans. Moscow Math. Soc., 26:95-132, 1972.
    • (1972) Trans. Moscow Math. Soc , vol.26 , pp. 95-132
    • Tempelman, A.A.1
  • 472
    • 0000661763 scopus 로고    scopus 로고
    • The theory of Rayleigh's principle as applied to continuous systems
    • G. Temple. The theory of Rayleigh's principle as applied to continuous systems. Proc. Roy. Soc. London A, 119:276-293, 1028.
    • Proc. Roy. Soc. London A , vol.119 , Issue.276-293 , pp. 1028
    • Temple, G.1
  • 473
    • 0003448985 scopus 로고
    • Springer-Verlag, Vienna, second edition, Quantenmechanik von Atomen und Molekülen
    • W. Thirring. Lehrbuch der mathematischen Physik. Band S. Springer-Verlag, Vienna, second edition, 1994. Quantenmechanik von Atomen und Molekülen.
    • (1994) Lehrbuch der mathematischen Physik. Band S
    • Thirring, W.1
  • 474
    • 0000485145 scopus 로고
    • Time-dependent approach to scattering from impurities in a crystal
    • L. Thomas. Time-dependent approach to scattering from impurities in a crystal. Commun. Math. Phys., 33:335-343, 1973.
    • (1973) Commun. Math. Phys , vol.33 , pp. 335-343
    • Thomas, L.1
  • 475
    • 84972571649 scopus 로고
    • On spectra of random Schrödinger operators with magnetic fields
    • N. Ueki. On spectra of random Schrödinger operators with magnetic fields. Osaka J. Math., 31(1):177-187, 1994.
    • (1994) Osaka J. Math , vol.31 , Issue.1 , pp. 177-187
    • Ueki, N.1
  • 476
    • 33747843902 scopus 로고    scopus 로고
    • The universality classes in the parabolic Anderson model
    • R. van der Hofstad, W. König, and P. Mörters. The universality classes in the parabolic Anderson model. Comm. Math. Phys., 267(2):307-353, 2006.
    • (2006) Comm. Math. Phys , vol.267 , Issue.2 , pp. 307-353
    • van der Hofstad, R.1    König, W.2    Mörters, P.3
  • 477
    • 0002209976 scopus 로고
    • Gap-labelling theorems for Schrödinger operators on the square and cubic lattice
    • A. Van Eist. Gap-labelling theorems for Schrödinger operators on the square and cubic lattice. Rev. Math. Phys., 6(2):319-342, 1994.
    • (1994) Rev. Math. Phys , vol.6 , Issue.2 , pp. 319-342
    • Van Eist, A.1
  • 478
    • 33744833465 scopus 로고
    • Quelques proprietes generales de 1 integrale de configuration d un systeme de particules avec interaction
    • L. Van Hove. Quelques proprietes generales de 1 integrale de configuration d un systeme de particules avec interaction. Physica, 15:951-961, 1949.
    • (1949) Physica , vol.15 , pp. 951-961
    • Van Hove, L.1
  • 479
  • 480
    • 0036435121 scopus 로고    scopus 로고
    • Localization for random perturbations of periodic Schrödinger operators with regular Floquet eigenvalues
    • I. Veselić. Localization for random perturbations of periodic Schrödinger operators with regular Floquet eigenvalues. Ann. Henri Poincaré, 3(2):389-409, 2002. http://www.ma.utexas.edu/mpjirc/c/98/ 98-569.ps.gz.
    • (2002) Ann. Henri Poincaré , vol.3 , Issue.2 , pp. 389-409
    • Veselić, I.1
  • 481
    • 0042869687 scopus 로고    scopus 로고
    • Wegner estimate and the density of states of some indefinite alloy type Schrödinger operators
    • I. Veselić. Wegner estimate and the density of states of some indefinite alloy type Schrödinger operators. Lett. Math. Phys., 59(3):199-214, 2002. http://www.ma.utexas.edu/mp_arc/c/00/00-373.ps.gz.
    • (2002) Lett. Math. Phys , vol.59 , Issue.3 , pp. 199-214
    • Veselić, I.1
  • 482
    • 28644432682 scopus 로고    scopus 로고
    • Existence of the density of states for some alloy type models with single site potentials that change sign
    • Kluwer Acad. Publ, Dordrecht
    • I. Veselic. Existence of the density of states for some alloy type models with single site potentials that change sign. In Proceedings of the Conference "Applied Mathematics and Scientific Computing", June 2001, Dubrovnik, pages 293-303, Kluwer Acad. Publ., Dordrecht, 2003. http://arXiv.org/math-ph/0204031.
    • (2003) Proceedings of the Conference "Applied Mathematics and Scientific Computing", June 2001, Dubrovnik , pp. 293-303
    • Veselic, I.1
  • 483
    • 26644460378 scopus 로고    scopus 로고
    • Integrated density of states and Wegner estimates for random Schrödinger operators
    • I. Veselic. Integrated density of states and Wegner estimates for random Schrödinger operators. Contemp. Math., 340:98-184, 2004. http://arXiv.org/math-ph/0307062.
    • (2004) Contemp. Math , vol.340 , pp. 98-184
    • Veselic, I.1
  • 485
    • 15244343972 scopus 로고    scopus 로고
    • Spectral analysis of percolation Hamiltonians
    • I. Veselić. Spectral analysis of percolation Hamiltonians. Math. Ann., 331(4):841-865, 2005. httpp//arXiv.org/math-ph/0405006.
    • (2005) Math. Ann , vol.331 , Issue.4 , pp. 841-865
    • Veselić, I.1
  • 487
    • 37149030507 scopus 로고    scopus 로고
    • Lifshitz asymptotics for hamiltonians monotone in the randomness
    • I. Veselic. Lifshitz asymptotics for hamiltonians monotone in the randomness. Oberwolfach Rep., 4(1):380-382, 2007. http://www.arxiv.org/ abs/0708.0487.
    • (2007) Oberwolfach Rep , vol.4 , Issue.1 , pp. 380-382
    • Veselic, I.1
  • 488
    • 37149015304 scopus 로고
    • Développement asymptotique de la densité d'états pour l'opérateur de Schrödinger aléatoire avec champ magnétique
    • Exp, Ecole Polytech, Palaiseau
    • W.-M. Wang. Développement asymptotique de la densité d'états pour l'opérateur de Schrödinger aléatoire avec champ magnétique. In Séminaire sur les Équations aux Dérivées Partielles, 1992-1993, pages 20, Exp. No. XVIII. Ecole Polytech., Palaiseau, 1993.
    • (1993) Séminaire sur les Équations aux Dérivées Partielles, 1992-1993 , Issue.XVIII , pp. 20
    • Wang, W.-M.1
  • 489
    • 0031142034 scopus 로고    scopus 로고
    • Microlocalization, percolation, and Anderson localization for the magnetic Schrödinger operator with a random potential
    • l-26
    • W.-M. Wang. Microlocalization, percolation, and Anderson localization for the magnetic Schrödinger operator with a random potential. J. Funct. Anal., 146(1):l-26, 1997.
    • (1997) J. Funct. Anal , vol.146 , Issue.1
    • Wang, W.-M.1
  • 490
    • 0013289253 scopus 로고    scopus 로고
    • Supersymmetry and density of states of the magnetic Schrödinger operator with a random potential revisited
    • W.-M. Wang. Supersymmetry and density of states of the magnetic Schrödinger operator with a random potential revisited. Comm. Partial Differential Equations, 25(3-4):601-679, 2000.
    • (2000) Comm. Partial Differential Equations , vol.25 , Issue.3-4 , pp. 601-679
    • Wang, W.-M.1
  • 491
    • 0035629873 scopus 로고    scopus 로고
    • Localization and universality of Poisson statistics for the multidimensional Anderson model at weak disorder
    • W.-M. Wang. Localization and universality of Poisson statistics for the multidimensional Anderson model at weak disorder. Invent. Math., 146(2):365-398, 2001.
    • (2001) Invent. Math , vol.146 , Issue.2 , pp. 365-398
    • Wang, W.-M.1
  • 492
    • 0040341936 scopus 로고    scopus 로고
    • Doctoral thesis, Universität Erlangen-Nürnberg, Logos, Berlin
    • S. Warzel. On Lifshitz tails in magnetic fields. Doctoral thesis, Universität Erlangen-Nürnberg, Logos, Berlin, 2001.
    • (2001) On Lifshitz tails in magnetic fields
    • Warzel, S.1
  • 493
    • 0002037112 scopus 로고
    • Bounds on the DOS in disordered systems
    • F. Wegner. Bounds on the DOS in disordered systems. Z. Phys. B, 44:9-15, 1981.
    • (1981) Z. Phys. B , vol.44 , pp. 9-15
    • Wegner, F.1
  • 495
    • 0003543786 scopus 로고    scopus 로고
    • Lineare Operatoren in Hilberträumen
    • B. G. Teubner, Stuttgart
    • J. Weidmann. Lineare Operatoren in Hilberträumen. Teil 1. Mathematische Leitfäden. B. G. Teubner, Stuttgart, 2000.
    • (2000) Mathematische Leitfäden , Issue.TEIL 1
    • Weidmann, J.1
  • 498
    • 0002499666 scopus 로고
    • Recent work on sharp estimates in second order elliptic unique continuation problems
    • Stud. Adv. Math, CRC, Boca Raton, FL
    • T. H. Wolff. Recent work on sharp estimates in second order elliptic unique continuation problems. In Fourier analysis and partial differential equations (Miraflores de la Sierra, 1992), Stud. Adv. Math., pages 99-128. CRC, Boca Raton, FL, 1995.
    • (1995) Fourier analysis and partial differential equations (Miraflores de la Sierra, 1992) , pp. 99-128
    • Wolff, T.H.1
  • 499
    • 0003897651 scopus 로고
    • Translations of Mathematical Monographs, American Mathematical Society, Providence, Rhode Island, Russian original: Izdatel'stvo Sankt-Peterburgskogo Universiteta, St. Petersburg
    • D. Yafaev. Mathematical Scattering Theory. Translations of Mathematical Monographs, 105. American Mathematical Society, Providence, Rhode Island, 1992. [Russian original: Izdatel'stvo Sankt-Peterburgskogo Universiteta, St. Petersburg, 1994].
    • (1992) Mathematical Scattering Theory , vol.105
    • Yafaev, D.1
  • 500
    • 0036011525 scopus 로고    scopus 로고
    • Anderson localization for a multidimensional model including long range potentials and displacements
    • H. Zenk. Anderson localization for a multidimensional model including long range potentials and displacements. Rev. Math. Phys., 14(3):273-302, 2002.
    • (2002) Rev. Math. Phys , vol.14 , Issue.3 , pp. 273-302
    • Zenk, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.