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Volumn 268, Issue 3, 2006, Pages 673-686

On the structure of eigenfunctions corresponding to embedded eigenvalues of locally perturbed periodic graph operators

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EID: 33750329519     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-006-0105-2     Document Type: Article
Times cited : (52)

References (35)
  • 1
    • 0001534008 scopus 로고
    • Superconductivity of networks. A percolation approach to the effects of disorder
    • Alexander, S.: Superconductivity of networks. A percolation approach to the effects of disorder. Phys. Rev. B, 27, 1541-1557 (1985)
    • (1985) Phys. Rev. B , vol.27 , pp. 1541-1557
    • Alexander, S.1
  • 3
    • 0001868814 scopus 로고
    • A directional compactification of the complex Fermi surface
    • Bättig, D., Knörrer, H., Trubowitz, E.: A directional compactification of the complex Fermi surface, Compositio Math. 79(2), 205-229 (1991)
    • (1991) Compositio Math. , vol.79 , Issue.2 , pp. 205-229
    • Bättig, D.1    Knörrer, H.2    Trubowitz, E.3
  • 4
    • 0000746335 scopus 로고    scopus 로고
    • The spectrum of the continuous Laplacian on a graph
    • Cattaneo, C.: The spectrum of the continuous Laplacian on a graph. Monatsh. Math. 124, 215-235 (1997)
    • (1997) Monatsh. Math. , vol.124 , pp. 215-235
    • Cattaneo, C.1
  • 5
    • 0003882879 scopus 로고    scopus 로고
    • Providence R.I.: Amer. Math. Soc.
    • Chung, F.: Spectral Graph Theory. Providence R.I.: Amer. Math. Soc., 1997
    • (1997) Spectral Graph Theory
    • Chung, F.1
  • 6
    • 0003794206 scopus 로고
    • Schrödinger operators with applications to quantum mechanics and global geometry
    • Berlin: Springer Verlag
    • Cycon, H.L., Froese, R.G., Kirsch, W., Simon, B.: Schrödinger Operators With Applications to Quantum Mechanics and Global Geometry. Texts and Monographs in Physics, Berlin: Springer Verlag, 1987
    • (1987) Texts and Monographs in Physics
    • Cycon, H.L.1    Froese, R.G.2    Kirsch, W.3    Simon, B.4
  • 7
    • 0036386544 scopus 로고    scopus 로고
    • The spectral measure of certain elements of the complex group ring of a wreath product
    • Dicks, W., Schick, T.: The Spectral Measure of Certain Elements of the Complex Group Ring of a Wreath Product. Geometriae Dedicata 93, 121-137 (2002)
    • (2002) Geometriae Dedicata , vol.93 , pp. 121-137
    • Dicks, W.1    Schick, T.2
  • 10
    • 0001685320 scopus 로고    scopus 로고
    • A duality between Schrödinger operators on graphs and certain Jacobi matrices
    • Exner, P.: A duality between Schrödinger operators on graphs and certain Jacobi matrices. Ann. Inst. H. Poincaré Phys. Theor. 66(4), 359-371 (1997)
    • (1997) Ann. Inst. H. Poincaré Phys. Theor. , vol.66 , Issue.4 , pp. 359-371
    • Exner, P.1
  • 12
    • 0003231591 scopus 로고    scopus 로고
    • The lamplighter group as a group generated by a 2-state automaton, and its spectrum
    • Grigorchuk, R., Zuk, A.: The lamplighter group as a group generated by a 2-state automaton, and its spectrum. Geom. Dedicata 87, 209-244 (2001)
    • (2001) Geom. Dedicata , vol.87 , pp. 209-244
    • Grigorchuk, R.1    Zuk, A.2
  • 13
    • 0003195390 scopus 로고
    • Hyperbolic groups
    • Gersten, S.M. (ed.) MSRI Publ. 8, New York: Springer Verlag
    • Gromov, M.: Hyperbolic groups. In: Gersten, S.M. (ed.) Essays in Group Theory. MSRI Publ. 8, New York: Springer Verlag, 1987, pp 75-263
    • (1987) Essays in Group Theory , pp. 75-263
    • Gromov, M.1
  • 14
    • 0034704432 scopus 로고    scopus 로고
    • Hermitian symplectic geometry and extension theory
    • Harmer, M.: Hermitian symplectic geometry and extension theory. J. Phys. A: Math. Gen. 33, 9193-9203 (2000)
    • (2000) J. Phys. A: Math. Gen. , vol.33 , pp. 9193-9203
    • Harmer, M.1
  • 15
    • 51249175788 scopus 로고
    • A directional compactification of the complex Bloch variety
    • Knörrer, H., Trubowitz, J.: A directional compactification of the complex Bloch variety. Comment. Math. Helv. 65, 114-149 (1990)
    • (1990) Comment. Math. Helv. , vol.65 , pp. 114-149
    • Knörrer, H.1    Trubowitz, J.2
  • 16
    • 0033613617 scopus 로고    scopus 로고
    • Kirchhoff's rule for quantum wires
    • Kostrykin, V., Schrader, R.: Kirchhoff's rule for quantum wires. J. Phys. A 32, 595-630 (1999)
    • (1999) J. Phys. A , vol.32 , pp. 595-630
    • Kostrykin, V.1    Schrader, R.2
  • 17
    • 0942280576 scopus 로고
    • To the Floquet theory of periodic difference equations
    • Cetraro, Italy, C. Berenstein, D. Struppa, eds., Perth: EditEl
    • Kuchment, P.: To the Floquet theory of periodic difference equations. In: Geometrical and Algebraical Aspects in Several Complex Variables, Cetraro, Italy, 1989, C. Berenstein, D. Struppa, eds., Perth: EditEl, pp. 203-209
    • (1989) Geometrical and Algebraical Aspects in Several Complex Variables , pp. 203-209
    • Kuchment, P.1
  • 19
    • 0001325714 scopus 로고    scopus 로고
    • The mathematics of photonics crystals
    • Ch. 7, Bao, G., Cowsar, L., Masters, W. (eds.) Philadelphia: SIAM
    • Kuchment, P.: The Mathematics of Photonics Crystals, Ch. 7. In: Mathematical Modeling in Optical Science. Bao, G., Cowsar, L., Masters, W. (eds.) Philadelphia: SIAM, 2001, pp 207-272
    • (2001) Mathematical Modeling in Optical Science , pp. 207-272
    • Kuchment, P.1
  • 20
    • 0942280564 scopus 로고    scopus 로고
    • Differential and pseudo-differential operators on graphs as models of mesoscopic systems
    • Begehr, H., Gilbert, R., Wang, M.W. (eds). Dordretcht: Kluwer Acad. Publ.
    • Kuchment, P.: Differential and pseudo-differential operators on graphs as models of mesoscopic systems. In: Begehr, H., Gilbert, R., Wang, M.W. (eds) Analysis and Applications. Dordretcht: Kluwer Acad. Publ., 2003, pp 7-30
    • (2003) Analysis and Applications , pp. 7-30
    • Kuchment, P.1
  • 21
    • 0036804366 scopus 로고    scopus 로고
    • Graph models of wave propagation in thin structures
    • Kuchment, P.: Graph models of wave propagation in thin structures. Waves in Random Media 12(4), R1-R24 (2002)
    • (2002) Waves in Random Media , vol.12 , Issue.4
    • Kuchment, P.1
  • 22
    • 0942278598 scopus 로고    scopus 로고
    • Quantum graphs I. Some basic structures
    • Kuchment, P.: Quantum graphs I. Some basic structures. Waves in Random Media 14, S107-S128 (2004)
    • (2004) Waves in Random Media , vol.14
    • Kuchment, P.1
  • 23
    • 19944363603 scopus 로고    scopus 로고
    • On some spectral problems of mathematical physics
    • Conca, C., Manasevich, R., Uhlmann, G., Vogelius, M.S. (eds.) Partial Differential Equations and Inverse Problems, Providence, RI: Amer. Math. Soc.
    • Kuchment, P.: On some spectral problems of mathematical physics. In: Conca, C., Manasevich, R., Uhlmann, G., Vogelius, M.S. (eds.) Partial Differential Equations and Inverse Problems. Contemp. Math. 362, Providence, RI: Amer. Math. Soc., 2004
    • (2004) Contemp. Math. , vol.362
    • Kuchment, P.1
  • 24
    • 19944375123 scopus 로고    scopus 로고
    • Quantum graphs II. Some spectral properties of quantum and combinatorial graphs
    • Kuchment, P.: Quantum graphs II. Some spectral properties of quantum and combinatorial graphs. J. Phys. A 38, 4887-4900 (2005)
    • (2005) J. Phys. A , vol.38 , pp. 4887-4900
    • Kuchment, P.1
  • 25
    • 0002503979 scopus 로고    scopus 로고
    • On embedded eigenvalues of perturbed periodic Schrödinger operators
    • (Newark, DE), New York: Plenum
    • Kuchment, P., Vainberg, B.: On embedded eigenvalues of perturbed periodic Schrödinger operators. In: Spectral and scattering theory (Newark, DE, 1997), New York: Plenum, 1998, pp. 67-75
    • (1997) Spectral and Scattering Theory , pp. 67-75
    • Kuchment, P.1    Vainberg, B.2
  • 26
    • 0034353901 scopus 로고    scopus 로고
    • On absence of embedded eigenvalues for Schrödinger operators with perturbed periodic potentials
    • Kuchment. P., Vainberg, B.: On absence of embedded eigenvalues for Schrödinger operators with perturbed periodic potentials. Commun. Part. Diff. Equal. 25(9-10), 1809-1826 (2000)
    • (2000) Commun. Part. Diff. Equal. , vol.25 , Issue.9-10 , pp. 1809-1826
    • Kuchment, P.1    Vainberg, B.2
  • 27
    • 0005211998 scopus 로고
    • Non-uniqueness in Cauchy's problem for differential equations of elliptic type
    • Plis, A.: Non-uniqueness in Cauchy's problem for differential equations of elliptic type. J. Math. Mech. 9, 557-562 (1960)
    • (1960) J. Math. Mech. , vol.9 , pp. 557-562
    • Plis, A.1
  • 28
    • 19944378533 scopus 로고    scopus 로고
    • Quantum graphs and their applications
    • Kuchment, P. (ed.)
    • Quantum Graphs and Their Applications. Kuchment, P. (ed.) Special issue of Waves in Random Media 14(1), (2004)
    • (2004) Special Issue of Waves in Random Media , vol.14 , Issue.1
  • 30
    • 0000048256 scopus 로고
    • A test for the finiteness of the number of discrete levels introduced into the gaps of a continuous spectrum by perturbations of a periodic potential
    • Rofe-Beketov, ES.: A test for the finiteness of the number of discrete levels introduced into the gaps of a continuous spectrum by perturbations of a periodic potential. Sov. Math. Dokl. 5, 689-692 (1964)
    • (1964) Sov. Math. Dokl. , vol.5 , pp. 689-692
    • Rofe-Beketov, E.S.1
  • 31
    • 0001861181 scopus 로고
    • Spectrum perturbations, the Knezer-type constants and the effective mass of zones-type potentials
    • Sofia: Bulgarian Acad. of Sci.
    • Rofe-Beketov, F.S.: Spectrum perturbations, the Knezer-type constants and the effective mass of zones-type potentials. In: Constructive Theory of Functions'84, Sofia: Bulgarian Acad. of Sci., 1984, pp. 757-766
    • (1984) Constructive Theory of Functions'84 , pp. 757-766
    • Rofe-Beketov, F.S.1
  • 32
    • 33644794789 scopus 로고    scopus 로고
    • Radiation conditions for the difference Schrödinger operators
    • Shaban, W., Vainberg, B.: Radiation conditions for the difference Schrödinger operators. Applicable Anal. 80, 525-556 (2002)
    • (2002) Applicable Anal. , vol.80 , pp. 525-556
    • Shaban, W.1    Vainberg, B.2
  • 33
    • 0000485145 scopus 로고
    • Time dependent approach to scattering from impurities in a crystal
    • Thomas, L.E.: 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.E.1
  • 34
    • 0001156229 scopus 로고
    • Principles of radiation, limiting absorption and limiting amplitude in the general theory of partial differential equations
    • Vainberg, B.: Principles of radiation, limiting absorption and limiting amplitude in the general theory of partial differential equations. Russ. Mam. Surv. 21(3), 115-193 (1966)
    • (1966) Russ. Mam. Surv. , vol.21 , Issue.3 , pp. 115-193
    • Vainberg, B.1
  • 35
    • 51249187120 scopus 로고
    • Theory of Bloch waves
    • Wilcox, C.: Theory of Bloch waves. J. Anal. Math. 33, 146-167 (1978)
    • (1978) J. Anal. Math. , vol.33 , pp. 146-167
    • Wilcox, C.1


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