메뉴 건너뛰기




Volumn , Issue 571, 2004, Pages 107-130

A diamagnetic inequality for semigroup differences

Author keywords

[No Author keywords available]

Indexed keywords


EID: 3142685163     PISSN: 00754102     EISSN: None     Source Type: Journal    
DOI: 10.1515/crll.2004.036     Document Type: Article
Times cited : (51)

References (64)
  • 1
    • 0000127371 scopus 로고
    • Positive compact operators on Banach lattices
    • C. D. Aliprantis and O. Burkinshaw, Positive compact operators on Banach lattices, Math. Z. 174 (1980), no. 3, 289-298.
    • (1980) Math. Z. , vol.174 , Issue.3 , pp. 289-298
    • Aliprantis, C.D.1    Burkinshaw, O.2
  • 2
    • 84972547058 scopus 로고
    • Schrödinger operators with magnetic fields, I. General interactions
    • J. Avron, I. Herbst, and B. Simon, Schrödinger operators with magnetic fields, I. General interactions, Duke Math. J. 45 (1978), 847-883.
    • (1978) Duke Math. J. , vol.45 , pp. 847-883
    • Avron, J.1    Herbst, I.2    Simon, B.3
  • 3
    • 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 (1983), 369-391.
    • (1983) Duke Math. J. , vol.50 , pp. 369-391
    • Avron, J.1    Simon, B.2
  • 4
    • 0003417636 scopus 로고    scopus 로고
    • Operator algebras and quantum statistical mechanics. 2, Equilibrium states, Models in quantum statistical mechanics, Second edition
    • Springer-Verlag, Berlin
    • O. Bratteli and D. W. Robinson, Operator algebras and quantum statistical mechanics. 2, Equilibrium states, Models in quantum statistical mechanics, Second edition, Texts and Monographs in Physics, Springer-Verlag, Berlin 1997.
    • (1997) Texts and Monographs in Physics
    • Bratteli, O.1    Robinson, D.W.2
  • 5
    • 0002693424 scopus 로고
    • Self-averaging, decomposition, and asymptotic properties of the density of states for random Schrödinger operators with constant magnetic field
    • eds. H. Grabert, A. Inomata, L. S. Schulman, and U. Weiss, World Scientific, Singapore
    • K. Broderix, D. Hundertmark, and H. Leschke, Self-averaging, decomposition, and asymptotic properties of the density of states for random Schrödinger operators with constant magnetic field, in: Path integrals from meV to MeV, Tutzing 1993, eds. H. Grabert, A. Inomata, L. S. Schulman, and U. Weiss, World Scientific, Singapore 1993.
    • (1993) Path Integrals from MeV to MeV, Tutzing 1993
    • Broderix, K.1    Hundertmark, D.2    Leschke, H.3
  • 6
    • 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 (2000), no. 2, 181-225.
    • (2000) Rev. Math. Phys. , vol.12 , Issue.2 , pp. 181-225
    • Broderix, K.1    Hundertmark, D.2    Leschke, H.3
  • 7
    • 0013295927 scopus 로고
    • Spectral theory of random Schrödinger operators
    • Birkhäuser, Boston
    • R. Carmona and J. Lacroix, Spectral theory of random Schrödinger operators, Probability and its Applications, Birkhäuser, Boston 1990.
    • (1990) Probability and Its Applications
    • Carmona, R.1    Lacroix, J.2
  • 8
    • 0002221209 scopus 로고
    • Classical bounds and limits for energy distributions of Hamilton operators in electromagnetic fields
    • J. M. Combes, R. Schrader, and R. Seiler, Classical bounds and limits for energy distributions of Hamilton operators in electromagnetic fields, Ann. Physics 111 (1978), no. 1, 1-18.
    • (1978) Ann. Physics , vol.111 , Issue.1 , pp. 1-18
    • Combes, J.M.1    Schrader, R.2    Seiler, R.3
  • 11
    • 0002976168 scopus 로고
    • Heat kernels and spectral theory
    • Cambridge University Press, Cambridge
    • E. B. Davies, Heat kernels and spectral theory, Cambridge Tracts Math. 92, Cambridge University Press, Cambridge 1990.
    • (1990) Cambridge Tracts Math. , vol.92
    • Davies, E.B.1
  • 12
    • 0001508569 scopus 로고
    • Spectral properties of the Neumann Laplacian of horns
    • E. B. Davies and B. Simon, Spectral properties of the Neumann Laplacian of horns, Geom. Funct. Anal. 2 (1992), 105-117.
    • (1992) Geom. Funct. Anal. , vol.2 , pp. 105-117
    • Davies, E.B.1    Simon, B.2
  • 13
    • 51249184169 scopus 로고
    • Compact operators in Banach lattices
    • P. G. Dodds and D. H. Fremlin, Compact operators in Banach lattices, Israel J. Math. 34 (1979), no. 4, 287-320.
    • (1979) Israel J. Math. , vol.34 , Issue.4 , pp. 287-320
    • Dodds, P.G.1    Fremlin, D.H.2
  • 14
    • 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 (2001), no. 2, 335-371.
    • (2001) Math. Z. , vol.237 , Issue.2 , pp. 335-371
    • Doi, S.-I.1    Iwatsuka, A.2    Mine, T.3
  • 15
    • 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 (1986), no. 1, 169-175.
    • (1986) Stochastic Process. Appl. , vol.23 , Issue.1 , pp. 169-175
    • Droese, J.1    Kirsch, W.2
  • 16
    • 0000962398 scopus 로고
    • The free energy of a macroscopic system
    • M. Fisher, The free energy of a macroscopic system, Arch. Rat. Mech. Anal. 17 (1964), 377-410.
    • (1964) Arch. Rat. Mech. Anal. , vol.17 , pp. 377-410
    • Fisher, M.1
  • 17
    • 3142751643 scopus 로고    scopus 로고
    • Elliptic partial differential equations of second order
    • Springer, Berlin
    • D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order, Classics in Mathematics, Springer, Berlin 1998.
    • (1998) Classics in Mathematics
    • Gilbarg, D.1    Trudinger, N.2
  • 18
    • 0000620718 scopus 로고
    • The essential spectrum of Neumann Laplacians on some bounded singular domains
    • R. Hempel, L. Seco, and B. Simon, The essential spectrum of Neumann Laplacians on some bounded singular domains, J. Funct. Anal. 102 (1991), 448-483.
    • (1991) J. Funct. Anal. , vol.102 , pp. 448-483
    • Hempel, R.1    Seco, L.2    Simon, B.3
  • 19
    • 84972582297 scopus 로고
    • Domination of semigroups and generalization of Kato's inequality
    • H. Hess, R. Schrader, and D. A. Uhlenbrock, Domination of semigroups and generalization of Kato's inequality, Duke Math. J. 44 (1977), no. 4, 893-904.
    • (1977) Duke Math. J. , vol.44 , Issue.4 , pp. 893-904
    • Hess, H.1    Schrader, R.2    Uhlenbrock, D.A.3
  • 20
    • 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 (2001), no. 2, 229-254.
    • (2001) Comm. Math. Phys. , vol.221 , Issue.2 , pp. 229-254
    • Hupfer, T.1    Leschke, H.2    Müller, P.3    Warzel, S.4
  • 21
    • 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 (2001), no. 12, 1547-1581.
    • (2001) Rev. Math. Phys. , vol.13 , Issue.12 , pp. 1547-1581
    • Hupfer, T.1    Leschke, H.2    Müller, P.3    Warzel, S.4
  • 22
    • 51249191546 scopus 로고
    • Schrödinger operators with singular potentials
    • Proceedings of the International Symposium on Partial Differential Equations and the Geometry of Normed Linear Spaces, Jerusalem 1972
    • T. Kato, Schrödinger operators with singular potentials, Proceedings of the International Symposium on Partial Differential Equations and the Geometry of Normed Linear Spaces, Jerusalem 1972, Israel J. Math. 13 (1972), 135-148.
    • (1972) Israel J. Math. , vol.13 , pp. 135-148
    • Kato, T.1
  • 23
    • 0000818766 scopus 로고
    • Random Schrödinger operators. A course
    • Schrödinger operators (Sønderborg 1988), Springer, Berlin
    • W. Kirsch, Random Schrödinger operators. A course, Schrödinger operators (Sønderborg 1988), Lect. Notes Phys. 345, Springer, Berlin (1989), 264-370.
    • (1989) Lect. Notes Phys. , vol.345 , pp. 264-370
    • Kirsch, W.1
  • 24
    • 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 15 (1982), no. 7, 2139-2156.
    • (1982) J. Phys. A , vol.15 , Issue.7 , pp. 2139-2156
    • Kirsch, W.1    Martinelli, F.2
  • 25
    • 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 (1983), no. 4, 1255-1260.
    • (1983) Duke Math. J. , vol.50 , Issue.4 , pp. 1255-1260
    • Kirsch, W.1    Martinelli, F.2
  • 26
    • 0003131388 scopus 로고
    • A remark on a paper: "A compactness condition for linear operators of function spaces"
    • H. Leinfelder, A remark on a paper: "A compactness condition for linear operators of function spaces" (J. Oper. Th. 1 (1979), no. 1, 49-54) by L. D. Pitt, Bayreuther Math. Sehr. 11 (1982), 57-66.
    • (1979) J. Oper. Th. , vol.1 , Issue.1 , pp. 49-54
    • Leinfelder, H.1
  • 27
    • 3142720833 scopus 로고
    • H. Leinfelder, A remark on a paper: "A compactness condition for linear operators of function spaces" (J. Oper. Th. 1 (1979), no. 1, 49-54) by L. D. Pitt, Bayreuther Math. Sehr. 11 (1982), 57-66.
    • (1982) Bayreuther Math. Sehr. , vol.11 , pp. 57-66
    • Pitt, L.D.1
  • 28
    • 0001815299 scopus 로고
    • Schrödinger operators with singular magnetic vector potentials
    • H. Leinfelder and C. Simader, Schrödinger operators with singular magnetic vector potentials, Math. Z. 176 (1981), no. 1, 1-19.
    • (1981) Math. Z. , vol.176 , Issue.1 , pp. 1-19
    • Leinfelder, H.1    Simader, C.2
  • 29
    • 0003819707 scopus 로고
    • Translated from the Russian by Eugene Yankovsky, Wiley-Interscience Publication, John Wiley & Sons, New York
    • I. Lifshits, S. Gredeskul, and L. Pastur, Introduction to the theory of disordered systems, Translated from the Russian by Eugene Yankovsky, Wiley-Interscience Publication, John Wiley & Sons, New York 1988.
    • (1988) Introduction to the Theory of Disordered Systems
    • Lifshits, I.1    Gredeskul, S.2    Pastur, L.3
  • 30
    • 0031574595 scopus 로고    scopus 로고
    • Dominated semigroups with singular complex potentials
    • V. Liskevich and A. Manavi, Dominated semigroups with singular complex potentials, J. Funct. Anal. 151 (1997), no. 2, 281-305.
    • (1997) J. Funct. Anal. , vol.151 , Issue.2 , pp. 281-305
    • Liskevich, V.1    Manavi, A.2
  • 32
    • 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 (1993), no. 2, 197-214.
    • (1993) J. Math. Soc. Japan , vol.45 , Issue.2 , pp. 197-214
    • Matsumoto, H.1
  • 33
    • 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 (2001), no. 1, 136-152.
    • (2001) J. Funct. Anal. , vol.179 , Issue.1 , pp. 136-152
    • Nakamura, S.1
  • 34
    • 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 (1977), no. 1, 111-139.
    • (1977) Japan. J. Math. (N.S.) , vol.3 , Issue.1 , pp. 111-139
    • Nakao, S.1
  • 35
    • 21444449002 scopus 로고    scopus 로고
    • Invariance of closed convex sets and domination criteria for semigroups
    • E.-M. Ouhabaz, Invariance of closed convex sets and domination criteria for semigroups, Pot. Anal. 5 (1996), no. 6, 611-625.
    • (1996) Pot. Anal. , vol.5 , Issue.6 , pp. 611-625
    • Ouhabaz, E.-M.1
  • 36
    • 0007137847 scopus 로고
    • The Schrödinger equation with random potential
    • L. Pastur, The Schrödinger equation with random potential, Theor. Math. Phys. 6 (1971), 299-306, Russian original: Teoret. Mat. Fiz. 6 (1971), no. 3, 415-424.
    • (1971) Theor. Math. Phys. , vol.6 , pp. 299-306
    • Pastur, L.1
  • 37
    • 0007137847 scopus 로고
    • L. Pastur, The Schrödinger equation with random potential, Theor. Math. Phys. 6 (1971), 299-306, Russian original: Teoret. Mat. Fiz. 6 (1971), no. 3, 415-424.
    • (1971) Russian Original: Teoret. Mat. Fiz. , vol.6 , Issue.3 , pp. 415-424
  • 38
    • 34250250635 scopus 로고
    • Spectral properties of disordered systems in the one-body approximation
    • L. Pastur, Spectral properties of disordered systems in the one-body approximation, Comm. Math. Phys. 75 (1980), no. 2, 179-196.
    • (1980) Comm. Math. Phys. , vol.75 , Issue.2 , pp. 179-196
    • Pastur, L.1
  • 39
    • 0003782825 scopus 로고
    • Spectra of random and almost-periodic operators, fundamental principles of mathematical sciences
    • Springer, Berlin
    • L. Pastur and A. Figotin, Spectra of random and almost-periodic operators, Fundamental Principles of Mathematical Sciences, Grundl. Math. Wiss. 297, Springer, Berlin 1992.
    • (1992) Grundl. Math. Wiss. , vol.297
    • Pastur, L.1    Figotin, A.2
  • 40
    • 0003131388 scopus 로고
    • A compactness condition for linear operators of function spaces
    • L. D. Pitt, A compactness condition for linear operators of function spaces, J. Oper. Th. 1 (1979), no. 1, 49-54.
    • (1979) J. Oper. Th. , vol.1 , Issue.1 , pp. 49-54
    • Pitt, L.D.1
  • 44
    • 0004048496 scopus 로고
    • Path integral approach to quantum physics. An introduction
    • Springer-Verlag, Berlin
    • G. Roepstorff, Path integral approach to quantum physics. An introduction, Texts and Monographs in Physics, Springer-Verlag, Berlin 1994.
    • (1994) Texts and Monographs in Physics
    • Roepstorff, G.1
  • 45
    • 0003707206 scopus 로고    scopus 로고
    • Reprint of the 1989 edition, World Scientific River Edge, NJ; Imperial College Press, London
    • D. Ruelle, Statistical mechanics. Rigorous results, Reprint of the 1989 edition, World Scientific River Edge, NJ; Imperial College Press, London 1999.
    • (1999) Statistical Mechanics. Rigorous Results
    • Ruelle, D.1
  • 47
    • 0000488253 scopus 로고
    • Universal diamagnetism of spinless bose systems
    • B. Simon, Universal diamagnetism of spinless bose systems, Phys. Rev. Lett. 36 (1976), 1083-1084.
    • (1976) Phys. Rev. Lett. , vol.36 , pp. 1083-1084
    • Simon, B.1
  • 48
    • 0001518364 scopus 로고
    • An abstract Kato's inequality for generators of positivity preserving semi-groups
    • B. Simon, An abstract Kato's inequality for generators of positivity preserving semi-groups, Ind. Math. J. 26 (1977), 1067-1073.
    • (1977) Ind. Math. J. , vol.26 , pp. 1067-1073
    • Simon, B.1
  • 49
    • 0000941292 scopus 로고
    • A canonical decomposition for quadratic forms with applications to monotone convergence theorems
    • B. Simon, A canonical decomposition for quadratic forms with applications to monotone convergence theorems, J. Funct. Anal. 28 (1978), no. 3, 377-385.
    • (1978) J. Funct. Anal. , vol.28 , Issue.3 , pp. 377-385
    • Simon, B.1
  • 50
    • 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. Math. 30 (1978), no. 3, 268-281.
    • (1978) Adv. Math. , vol.30 , Issue.3 , pp. 268-281
    • Simon, B.1
  • 52
    • 0002596898 scopus 로고
    • Maximal and minimal Schrödinger forms
    • B. Simon, Maximal and minimal Schrödinger forms, J. Oper. Th. 1 (1979), 37-47.
    • (1979) J. Oper. Th. , vol.1 , pp. 37-47
    • Simon, B.1
  • 53
    • 0002093591 scopus 로고
    • Kato's inequality and the comparison of semi-groups
    • B. Simon, Kato's inequality and the comparison of semi-groups, J. Funct. Anal. 32 (1979), 97-101.
    • (1979) J. Funct. Anal. , vol.32 , pp. 97-101
    • Simon, B.1
  • 54
    • 84966201521 scopus 로고
    • The Neumann Laplacian of a jelly roll
    • B. Simon, The Neumann Laplacian of a jelly roll, Proc. Amer. Math. Soc. 114 (1992), 783-785.
    • (1992) Proc. Amer. Math. Soc. , vol.114 , pp. 783-785
    • Simon, B.1
  • 55
    • 0011027509 scopus 로고
    • Admissible and regular potentials for Schrödinger forms
    • P. Stollmann, Admissible and regular potentials for Schrödinger forms, J. Oper. Th. 18 (1987), no. 1, 139-151.
    • (1987) J. Oper. Th. , vol.18 , Issue.1 , pp. 139-151
    • Stollmann, P.1
  • 57
    • 84972526612 scopus 로고
    • Stochastic differential equations with reflecting boundary condition in convex regions
    • H. Tanaka, Stochastic differential equations with reflecting boundary condition in convex regions, Hiroshima Math. J. 9 (1979), no. 1, 163-177.
    • (1979) Hiroshima Math. J. , vol.9 , Issue.1 , pp. 163-177
    • Tanaka, H.1
  • 58
    • 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 (1994), no. 1, 177-187.
    • (1994) Osaka J. Math. , vol.31 , Issue.1 , pp. 177-187
    • Ueki, N.1
  • 59
    • 38249040541 scopus 로고
    • Absorption semigroups, their generators, and Schrödinger semigroups
    • J. Voigt, Absorption semigroups, their generators, and Schrödinger semigroups, J. Funct. Anal. 67 (1986), no. 2, 167-205.
    • (1986) J. Funct. Anal. , vol.67 , Issue.2 , pp. 167-205
    • Voigt, J.1
  • 60
    • 0000912714 scopus 로고
    • Absorption semigroups
    • J. Voigt, Absorption semigroups, J. Oper. Th. 20 (1988), no. 1, 117-131.
    • (1988) J. Oper. Th. , vol.20 , Issue.1 , pp. 117-131
    • Voigt, J.1
  • 61
    • 0002182320 scopus 로고
    • Stetige Abhängigkeit der Eigenwerte und Eigenfunktionen elliptischer Differentialoperatoren vom Gebiet
    • in German
    • J. Weidmann, Stetige Abhängigkeit der Eigenwerte und Eigenfunktionen elliptischer Differentialoperatoren vom Gebiet, Continuous dependence of eigenvalues and eigenfunctions of elliptic differential operators on the domain, Math. Scand. 54 (1984), no. 1, 51-69 (in German).
    • (1984) Math. Scand. , vol.54 , Issue.1 , pp. 51-69
    • Weidmann, J.1
  • 62
    • 0001117305 scopus 로고
    • Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differentialgleichungen (mit einer Anwendung auf die Theorie der Hohlraumstrahlung)
    • in German
    • H. Weyl, Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differentialgleichungen (mit einer Anwendung auf die Theorie der Hohlraumstrahlung), Math. Ann. 71 (1912), 441-479 (in German).
    • (1912) Math. Ann. , vol.71 , pp. 441-479
    • Weyl, H.1
  • 63
    • 0000532811 scopus 로고
    • Reflected Brownian motion: Hunt processes and semimartingale representation
    • Barcelona Seminar on Stochastic Analysis (St. Feliu de Guxols 1991), Birkhäuser, Basel
    • R. J. Williams, Reflected Brownian motion: Hunt processes and semimartingale representation, in: Barcelona Seminar on Stochastic Analysis (St. Feliu de Guxols 1991), Progr. Probab. 32, Birkhäuser, Basel (1993), 216-221.
    • (1993) Progr. Probab. , vol.32 , pp. 216-221
    • Williams, R.J.1
  • 64
    • 0042390727 scopus 로고
    • On reflecting Brownian motion - A weak convergence approach
    • R. J. Williams and W. A. Zheng, On reflecting Brownian motion - a weak convergence approach, Ann. Inst. H. Poincaré Probab. Statist. 26 (1990), no. 3, 461-488.
    • (1990) Ann. Inst. H. Poincaré Probab. Statist. , vol.26 , Issue.3 , pp. 461-488
    • Williams, R.J.1    Zheng, W.A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.