메뉴 건너뛰기




Volumn 4, Issue 5, 1997, Pages 719-723

The absolutely continuous spectrum of one-dimensional Schrödinger operators with decaying potentials

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0031541443     PISSN: 10732780     EISSN: None     Source Type: Journal    
DOI: 10.4310/MRL.1997.v4.n5.a9     Document Type: Article
Times cited : (22)

References (28)
  • 1
    • 0001388814 scopus 로고
    • Scattering with long range potentials
    • Amer. Math. Soc., Providence, Rhode Island
    • 1. P. K. Alsholm and T. Kato, Scattering with long range potentials, Partial Diff. Eq., Proc. Symp. Pure Math. Vol. 23, Amer. Math. Soc., Providence, Rhode Island, 1973, 393-399.
    • (1973) Partial Diff. Eq., Proc. Symp. Pure Math. , vol.23 , pp. 393-399
    • Alsholm, P.K.1    Kato, T.2
  • 2
    • 84968502687 scopus 로고
    • Absolute continuity of Hamiltonians with von Neumann-Wigner potentials
    • 2. H. Behncke, Absolute continuity of Hamiltonians with von Neumann-Wigner potentials, Proc. Amer. Math. Soc. 111 (1991), 373-384.
    • (1991) Proc. Amer. Math. Soc. , vol.111 , pp. 373-384
    • Behncke, H.1
  • 3
    • 36749111712 scopus 로고
    • Spectral and scattering theory for adiabatic oscillator and related potentials
    • 3. M. Ben Artzi and A. Devinatz, Spectral and scattering theory for adiabatic oscillator and related potentials, J. Math. Phys. 20 (1979), 594-607.
    • (1979) J. Math. Phys. , vol.20 , pp. 594-607
    • Ben Artzi, M.1    Devinatz, A.2
  • 4
    • 34250445134 scopus 로고
    • Wave operators for Schrödinger equation with a slowly decreasing potentials
    • 4. V. S. Buslaev and V. B. Matveev, Wave operators for Schrödinger equation with a slowly decreasing potentials, Theor. Math. Phys. 2 (1970), 266-274.
    • (1970) Theor. Math. Phys. , vol.2 , pp. 266-274
    • Buslaev, V.S.1    Matveev, V.B.2
  • 6
    • 0001067228 scopus 로고
    • Apparition of purely singular continuous spectrum in a class of random Schrödinger operators
    • 6. F. Delyon, Apparition of purely singular continuous spectrum in a class of random Schrödinger operators, J. Statist. Phys. 40 (1985), 621-630.
    • (1985) J. Statist. Phys. , vol.40 , pp. 621-630
    • Delyon, F.1
  • 7
    • 0001180136 scopus 로고
    • From power pure point to continuous spectrum in disordered systems
    • 7. F. Delyon, B. Simon, and B. Souillard, From power pure point to continuous spectrum in disordered systems, Ann. Inst. H. Poincare 42 (1985), 283-309.
    • (1985) Ann. Inst. H. Poincare , vol.42 , pp. 283-309
    • Delyon, F.1    Simon, B.2    Souillard, B.3
  • 8
    • 0003245993 scopus 로고
    • Schrödinger type operators with continuous spectra
    • Pitman, London
    • 8. M. S. P. Eastham and H. Kalf, Schrödinger type operators with continuous spectra, Research Notes in Mathematics, vol. 65, Pitman, London, 1982.
    • (1982) Research Notes in Mathematics , vol.65
    • Eastham, M.S.P.1    Kalf, H.2
  • 9
    • 0010958011 scopus 로고
    • Absolutely continuous spectra of second-order differential operators with short and long range potentials
    • 9. D. B. Hinton and J. K. Shaw, Absolutely continuous spectra of second-order differential operators with short and long range potentials, SIAM J. Math. Anal. 17 (1986), 182-196.
    • (1986) SIAM J. Math. Anal. , vol.17 , pp. 182-196
    • Hinton, D.B.1    Shaw, J.K.2
  • 10
    • 0002785570 scopus 로고
    • The existence of wave operators in scattering theory
    • 10. L. Hörmander, The existence of wave operators in scattering theory, Math. Z. 146 (1976), 69-91.
    • (1976) Math. Z. , vol.146 , pp. 69-91
    • Hörmander, L.1
  • 11
    • 0040523358 scopus 로고    scopus 로고
    • Absolutely continuous spectrum of one-dimensional Schrödinger operators and Jacobi matrices with slowly decreasing potentials
    • 11. A. Kiselev, Absolutely continuous spectrum of one-dimensional Schrödinger operators and Jacobi matrices with slowly decreasing potentials, Commun. Math. Phys. 179 (1996), 377-400.
    • (1996) Commun. Math. Phys. , vol.179 , pp. 377-400
    • Kiselev, A.1
  • 12
    • 85033086965 scopus 로고    scopus 로고
    • Stability of the absolutely continuous spectrum of the Schrödinger equation under perturbations by slowly decreasing potentials and a.e. convergence of integral operators
    • to appear
    • 12. _, Stability of the absolutely continuous spectrum of the Schrödinger equation under perturbations by slowly decreasing potentials and a.e. convergence of integral operators, Duke Math. J., (to appear).
    • Duke Math. J.
  • 13
    • 0001779113 scopus 로고    scopus 로고
    • Modified Prüfer and EFGP transforms and the spectral analysis of one-dimensional Schrödinger operators
    • to appear
    • 13. A. Kiselev, Y. Last, and B. Simon, Modified Prüfer and EFGP transforms and the spectral analysis of one-dimensional Schrödinger operators, Commun. Math. Phys., (to appear).
    • Commun. Math. Phys.
    • Kiselev, A.1    Last, Y.2    Simon, B.3
  • 14
    • 0001261704 scopus 로고
    • One-dimensional Schrödinger operators with random decaying potentials
    • 14. S. Kotani and N. Ushiroya, One-dimensional Schrödinger operators with random decaying potentials, Commun. Math. Phys. 115 (1988), 247-266.
    • (1988) Commun. Math. Phys. , vol.115 , pp. 247-266
    • Kotani, S.1    Ushiroya, N.2
  • 15
    • 0010957560 scopus 로고
    • Wave operators and positive eigenvalues for Schrödinger equation with oscillating potential
    • 15. V. B. Matveev, Wave operators and positive eigenvalues for Schrödinger equation with oscillating potential, Theor. Math. Phys. 15 (1973), 574-583.
    • (1973) Theor. Math. Phys. , vol.15 , pp. 574-583
    • Matveev, V.B.1
  • 17
    • 85033081000 scopus 로고    scopus 로고
    • private communication and in preparation
    • 17. _, private communication and in preparation.
  • 18
    • 0001062331 scopus 로고
    • Dense point spectra of Schrödinger and Dirac operators
    • 18. S. N. Naboko, Dense point spectra of Schrödinger and Dirac operators, Theor. and Math. Phys. 68 (1986), 646-653.
    • (1986) Theor. and Math. Phys. , vol.68 , pp. 646-653
    • Naboko, S.N.1
  • 20
    • 85033078275 scopus 로고    scopus 로고
    • Embedded singular continuous spectrum for one-dimensional Schrödinger operators
    • 20. C. Remling, Embedded singular continuous spectrum for one-dimensional Schrödinger operators, submitted to Trans. Amer. Math. Soc.
    • Trans. Amer. Math. Soc.
    • Remling, C.1
  • 21
    • 85033096742 scopus 로고    scopus 로고
    • The absolutely continuous spectrum of one-dimensional Schrödinger operators with decaying potentials
    • 21. _, The absolutely continuous spectrum of one-dimensional Schrödinger operators with decaying potentials, to be submitted to Commun. Math. Phys.
    • Commun. Math. Phys.
  • 22
    • 0000364033 scopus 로고
    • Some Jacobi matrices with decaying potentials and dense point spectrum
    • 22. B. Simon, Some Jacobi matrices with decaying potentials and dense point spectrum, Commun. Math. Phys. 87 (1982), 253-258.
    • (1982) Commun. Math. Phys. , vol.87 , pp. 253-258
    • Simon, B.1
  • 23
    • 21444433761 scopus 로고    scopus 로고
    • Bounded eigenfunctions and absolutely continuous spectra for one-dimensional Schrödinger operators
    • 23. _, Bounded eigenfunctions and absolutely continuous spectra for one-dimensional Schrödinger operators, Proc. Amer. Math. Soc. 124 (1996), 3361-3369.
    • (1996) Proc. Amer. Math. Soc. , vol.124 , pp. 3361-3369
  • 24
    • 21444440696 scopus 로고    scopus 로고
    • Some Schrödinger operators with dense point spectrum
    • 24. _, Some Schrödinger operators with dense point spectrum, Proc. Amer. Math. Soc. 125 (1997), 203-208.
    • (1997) Proc. Amer. Math. Soc. , vol.125 , pp. 203-208
  • 25
    • 0001363089 scopus 로고
    • Bounded solutions and absolute continuity of Sturm-Liouville operators
    • 25. G. Stolz, Bounded solutions and absolute continuity of Sturm-Liouville operators, J. Math. Anal. Appl. 169 (1992), 210-228.
    • (1992) J. Math. Anal. Appl. , vol.169 , pp. 210-228
    • Stolz, G.1
  • 26
    • 0000424987 scopus 로고
    • Über merkwürdige diskrete Eigenwerte
    • 26. J. von Neumann and E. Wigner, Über merkwürdige diskrete Eigenwerte, Z. Phys. 30 (1929), 465-467.
    • (1929) Z. Phys. , vol.30 , pp. 465-467
    • Von Neumann, J.1    Wigner, E.2
  • 27
    • 0001579357 scopus 로고
    • Zur Spektraltheorie von Sturm-Liouville Operatoren
    • 27. J. Weidmann, Zur Spektraltheorie von Sturm-Liouville Operatoren, Math. Z. 98 (1967), 268-301.
    • (1967) Math. Z. , vol.98 , pp. 268-301
    • Weidmann, J.1
  • 28
    • 0000327274 scopus 로고
    • Schrödinger operators with rapidly oscilating central potentials
    • 28. D. A. W. White, Schrödinger operators with rapidly oscilating central potentials, Trans. Amer. Math. Soc. 275 (1983), 641-677.
    • (1983) Trans. Amer. Math. Soc. , vol.275 , pp. 641-677
    • White, D.A.W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.