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Volumn 25, Issue 9-10, 2000, Pages 1809-1826

On absence of embedded eigenvalues for Schrödinger operators with perturbed periodic potentials

Author keywords

Embedded eigenvalues; Periodic potential; Schr dinger operator

Indexed keywords


EID: 0034353901     PISSN: 03605302     EISSN: None     Source Type: Journal    
DOI: 10.1080/03605300008821568     Document Type: Article
Times cited : (50)

References (41)
  • 1
    • 0028444852 scopus 로고
    • On the existence of eigenvalues of a divergence form operator A + λB in a gap of σ(A)
    • S. Alama, M. Avellaneda, P. A. Deift, and R. Hempel, On the existence of eigenvalues of a divergence form operator A + λB in a gap of σ(A), Asymptotic Anal. 8(1994), no.4, 311-314.
    • (1994) Asymptotic Anal. , vol.8 , Issue.4 , pp. 311-314
    • Alama, S.1    Avellaneda, M.2    Deift, P.A.3    Hempel, R.4
  • 2
    • 0000430599 scopus 로고
    • Eigenvalue branches of the Schrödinger operator H - λW in a gap of σ(H)
    • S. Alama, P. A. Deift, and R. Hempel, Eigenvalue branches of the Schrödinger operator H - λW in a gap of σ(H), Commun. Math. Phys. 121(1989), 291-321.
    • (1989) Commun. Math. Phys. , vol.121 , pp. 291-321
    • Alama, S.1    Deift, P.A.2    Hempel, R.3
  • 3
    • 0001868814 scopus 로고
    • A directional compactification of the complex fermi surface
    • D. Bättig, H. Knörrer, and E. Trubowitz, A directional compactification of the complex Fermi surface, Compositio Math. 79(1991), no.2, 205-229.
    • (1991) Compositio Math. , vol.79 , Issue.2 , pp. 205-229
    • Bättig, D.1    Knörrer, H.2    Trubowitz, E.3
  • 4
    • 0001897470 scopus 로고    scopus 로고
    • The discrete spectrum of the periodic Schrödinger operator perturbed by a decreasing potential
    • M. S. Birman, The discrete spectrum of the periodic Schrödinger operator perturbed by a decreasing potential, Algebra i Analiz 8(1996), no.1, 3-20.
    • (1996) Algebra i Analiz , vol.8 , Issue.1 , pp. 3-20
    • Birman, M.S.1
  • 5
    • 0001399811 scopus 로고
    • On the spectrum of singular boundary value problems
    • M. S. Birman, On the spectrum of singular boundary value problems, Mat. Sbornik 55(1961), no.2, 125-173.
    • (1961) Mat. Sbornik , vol.55 , Issue.2 , pp. 125-173
    • Birman, M.S.1
  • 6
    • 0000478255 scopus 로고
    • On the discrete spectrum in the gaps of a perturbed periodic second order operator
    • M. S. Birman, On the discrete spectrum in the gaps of a perturbed periodic second order operator, Funct. Anal. Appl. 25(1991), 158-161.
    • (1991) Funct. Anal. Appl. , vol.25 , pp. 158-161
    • Birman, M.S.1
  • 9
    • 0001538638 scopus 로고
    • On the existence of eigenvalues of the Schrödinger operator H - λW in a gap of σ(H)
    • P. A. Deift and R. Hempel, On the existence of eigenvalues of the Schrödinger operator H - λW in a gap of σ(H), Commun. Math. Phys. 103(1986), 461-490.
    • (1986) Commun. Math. Phys. , vol.103 , pp. 461-490
    • Deift, P.A.1    Hempel, R.2
  • 13
    • 0001123378 scopus 로고
    • Expansion in eigenfunctions of an equation with periodic coefficients
    • I.M. Gelfand, Expansion in eigenfunctions of an equation with periodic coefficients, Dokl. Akad. Nauk SSSR 73(1950), 1117-1120.
    • (1950) Dokl. Akad. Nauk SSSR , vol.73 , pp. 1117-1120
    • Gelfand, I.M.1
  • 14
    • 17644437865 scopus 로고    scopus 로고
    • The Mourre theory for analytically fibered operators
    • C. Gerard and F. Nier, The Mourre theory for analytically fibered operators, J. Funct. Anal. 152(1998), no.1, 202-219.
    • (1998) J. Funct. Anal. , vol.152 , Issue.1 , pp. 202-219
    • Gerard, C.1    Nier, F.2
  • 15
    • 0001383853 scopus 로고
    • On a theorem of Deift and Hempel
    • F. Gesztesy and B. Simon, On a theorem of Deift and Hempel, Commun. Math. Phys. 116(1988), 503-505.
    • (1988) Commun. Math. Phys. , vol.116 , pp. 503-505
    • Gesztesy, F.1    Simon, B.2
  • 18
    • 0001787082 scopus 로고
    • Eigenvalue branches of the Schrödinger operator H ± λW in a spectral gap of H
    • R. Hempel, Eigenvalue branches of the Schrödinger operator H ± λW in a spectral gap of H, J. Reine Angew. Math. 399(1989), 38-59.
    • (1989) J. Reine Angew. Math. , vol.399 , pp. 38-59
    • Hempel, R.1
  • 20
    • 51249163667 scopus 로고
    • Resonances for perturbations of a semi-classical periodic Schrödinger operator
    • F. Klopp, Resonances for perturbations of a semi-classical periodic Schrödinger operator, Arkiv för matematik, 32(1994), 323-371.
    • (1994) Arkiv För Matematik , vol.32 , pp. 323-371
    • Klopp, F.1
  • 21
    • 51249175788 scopus 로고
    • A directional compactification of the complex bloch variety
    • H. Knörrer and J. Trubowitz, A directional compactification of the complex Bloch variety, Comment. Math. Helv. 65(1990), 114-149.
    • (1990) Comment. Math. Helv. , vol.65 , pp. 114-149
    • Knörrer, H.1    Trubowitz, J.2
  • 23
    • 0002503979 scopus 로고    scopus 로고
    • On embedded eigenvalues of perturbed periodic Schrödinger operators
    • Newark, DE, 1997, Plenum, New York
    • P. Kuchment and B. Vainberg, On embedded eigenvalues of perturbed periodic Schrödinger operators, in Spectral and scattering theory (Newark, DE, 1997), 67-75, Plenum, New York,1998.
    • (1998) Spectral and Scattering Theory , pp. 67-75
    • Kuchment, P.1    Vainberg, B.2
  • 25
    • 4243750248 scopus 로고    scopus 로고
    • Asymptotic formulas with remainder estimates for eigenvalue branches of the Schrödinger operator H - λW in a gap of H
    • S. Z. Levendorskii, Asymptotic formulas with remainder estimates for eigenvalue branches of the Schrödinger operator H - λW in a gap of H, Trans. AMS.
    • Trans. AMS
    • Levendorskii, S.Z.1
  • 26
    • 0001966207 scopus 로고    scopus 로고
    • An asymptotic formula for the number of eigenvalue branches of a divergence form operator A + λB in a spectral gap of A
    • S. Z. Levendorskii and S. I. Boyarchenko, An asymptotic formula for the number of eigenvalue branches of a divergence form operator A + λB in a spectral gap of A, Comm. PDE.
    • Comm. PDE
    • Levendorskii, S.Z.1    Boyarchenko, S.I.2
  • 27
    • 0001711511 scopus 로고
    • Lower bounds for the number of eigenvalue branches for the Schrödinger operator H - λW in a gap of H: The case of indefinite W
    • S. Z. Levendorskii, Lower bounds for the number of eigenvalue branches for the Schrödinger operator H - λW in a gap of H: the case of indefinite W, Comm. PDE 20(1995), no.5-6, 827-854.
    • (1995) Comm. PDE , vol.20 , Issue.5-6 , pp. 827-854
    • Levendorskii, S.Z.1
  • 28
    • 0003281219 scopus 로고
    • Distribution of zeros of entire functions
    • Amer. Math. Soc., Providence, RI
    • B. Levin, Distribution of Zeros of Entire Functions, Transl. Math. Monogr. v.5, Amer. Math. Soc., Providence, RI 1964.
    • (1964) Transl. Math. Monogr. , vol.5
    • Levin, B.1
  • 29
    • 0000134587 scopus 로고
    • On the possible rate of decay at infinity of solutions of second order partial differential equations
    • V. Meshkov, On the possible rate of decay at infinity of solutions of second order partial differential equations, Mat. Sbornik, 182(1991). no.3, 364-383. English translation in Math. USSR Sbornik 72(1992), no.2, 343-351.
    • (1991) Mat. Sbornik , vol.182 , Issue.3 , pp. 364-383
    • Meshkov, V.1
  • 30
    • 0001966209 scopus 로고
    • V. Meshkov, On the possible rate of decay at infinity of solutions of second order partial differential equations, Mat. Sbornik, 182(1991). no.3, 364-383. English translation in Math. USSR Sbornik 72(1992), no.2, 343-351.
    • (1992) Math. USSR Sbornik , vol.72 , Issue.2 , pp. 343-351
  • 31
    • 0003234244 scopus 로고
    • Intorduction to the theory of analytic spaces
    • Springer Verlag, Berlin
    • R. Narasimhan, Intorduction to the Theory of Analytic Spaces, Lect. Notes in Math., v. 25, Springer Verlag, Berlin 1966.
    • (1966) Lect. Notes in Math. , vol.25
    • Narasimhan, R.1
  • 32
    • 0001170610 scopus 로고
    • Partial differential equations with periodic coefficients and bloch waves in crystals
    • F. Odeh, J.B. Keller, Partial differential equations with periodic coefficients and Bloch waves in crystals, J. Math. Phys. 5(1964), 1499-1504.
    • (1964) J. Math. Phys. , vol.5 , pp. 1499-1504
    • Odeh, F.1    Keller, J.B.2
  • 33
    • 0001709943 scopus 로고    scopus 로고
    • private communication
    • V. Papanicolaou, private communication, 1998.
    • (1998)
    • Papanicolaou, V.1
  • 34
    • 0002172409 scopus 로고
    • Eigenvalue asymptotics for the Schrödinger operator with perturbed periodic potential
    • G. D. Raikov, Eigenvalue asymptotics for the Schrödinger operator with perturbed periodic potential, Invent. Math. 110(1992), 75-93.
    • (1992) Invent. Math. , vol.110 , pp. 75-93
    • Raikov, G.D.1
  • 36
    • 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
    • F. S. Rofe-Beketov, 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, Soviet Math. Dokl. 5(1964), 689-692.
    • (1964) Soviet Math. Dokl. , vol.5 , pp. 689-692
    • Rofe-Beketov, F.S.1
  • 37
    • 0001861181 scopus 로고
    • Spectrum perturbations, the knezer-type constants and the effective mass of zones-type potentials
    • Sofia
    • F. S. Rofe-Beketov, Spectrum perturbations, the Knezer-type constants and the effective mass of zones-type potentials, in Constructive Theory of Functions'84, Sofia 1984, p.757-766.
    • (1984) Constructive Theory of Functions'84 , pp. 757-766
    • Rofe-Beketov, F.S.1
  • 38
    • 0001126677 scopus 로고
    • Weyl asymptotics for the discrete spectrum of the perturbed hill operator
    • A. Y. Sobolev, Weyl asymptotics for the discrete spectrum of the perturbed Hill operator, Adv. Sov. Math. 7(1991), 159-178.
    • (1991) Adv. Sov. Math. , vol.7 , pp. 159-178
    • Sobolev, A.Y.1
  • 40
    • 0001156229 scopus 로고
    • Principles of radiation, limiting absorption and limiting amplitude in the general theory of partial differential equations
    • B. Vainberg, Principles of radiation, limiting absorption and limiting amplitude in the general theory of partial differential equations, Russian Math. Surveys 21(1966), no 3, 115-193.
    • (1966) Russian Math. Surveys , vol.21 , Issue.3 , pp. 115-193
    • Vainberg, B.1
  • 41
    • 51249187120 scopus 로고
    • Theory of bloch waves
    • C. Wilcox, Theory of Bloch waves, J. Anal. Math. 33(1978), 146-167.
    • (1978) J. Anal. Math. , vol.33 , pp. 146-167
    • Wilcox, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.