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Volumn , Issue 38, 2002, Pages 2029-2061

Perturbations of one-dimensional Schrödinger operators preserving the absolutely continuous spectrum

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EID: 0036401805     PISSN: 10737928     EISSN: None     Source Type: Journal    
DOI: 10.1155/s1073792802204250     Document Type: Article
Times cited : (49)

References (46)
  • 1
    • 0003283055 scopus 로고
    • Handbook of mathematical functions with formulas, graphs, and mathematical tables
    • U.S. Government Printing Office, District of Columbia
    • M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Bureau of Standards Applied Mathematics Series, vol. 55, U.S. Government Printing Office, District of Columbia, 1964.
    • (1964) Bureau of Standards Applied Mathematics Series , vol.55
    • Abramowitz, M.1    Stegun, I.A.2
  • 2
    • 0347334708 scopus 로고    scopus 로고
    • Absolutely continuous spectrum for one-dimensional Schrödinger operators with slowly decaying potentials: Some optimal results
    • M. Christ and A. Kiselev, Absolutely continuous spectrum for one-dimensional Schrödinger operators with slowly decaying potentials: Some optimal results, J. Amer. Math. Soc. 11 (1998), no. 4, 771-797.
    • (1998) J. Amer. Math. Soc. , vol.11 , Issue.4 , pp. 771-797
    • Christ, M.1    Kiselev, A.2
  • 3
    • 0035531899 scopus 로고    scopus 로고
    • WKB and spectral analysis of one-dimensional Schrödinger operators with slowly varying potentials
    • _, WKB and spectral analysis of one-dimensional Schrödinger operators with slowly varying potentials, Comm. Math. Phys. 218 (2001), no. 2, 245-262.
    • (2001) Comm. Math. Phys. , vol.218 , Issue.2 , pp. 245-262
  • 4
    • 0035255585 scopus 로고    scopus 로고
    • WKB asymptotic behavior of almost all generalized eigenfunctions for one-dimensional Schrödinger operators with slowly decaying potentials
    • _, WKB asymptotic behavior of almost all generalized eigenfunctions for one-dimensional Schrödinger operators with slowly decaying potentials, J. Funct. Anal. 179 (2001), no. 2, 426-447.
    • (2001) J. Funct. Anal. , vol.179 , Issue.2 , pp. 426-447
  • 7
    • 0031541443 scopus 로고    scopus 로고
    • The absolutely continuous spectrum of one-dimensional Schrödinger operators with decaying potentials
    • M. Christ, A. Kiselev, and C. Remling, The absolutely continuous spectrum of one-dimensional Schrödinger operators with decaying potentials, Math. Res. Lett. 4 (1997), no. 5, 719-723.
    • (1997) Math. Res. Lett. , vol.4 , Issue.5 , pp. 719-723
    • Christ, M.1    Kiselev, A.2    Remling, C.3
  • 9
    • 0007035802 scopus 로고    scopus 로고
    • On the absolutely continuous spectrum of one-dimensional Schrödinger operators with square summable potentials
    • P. Deift and R. Killip, On the absolutely continuous spectrum of one-dimensional Schrödinger operators with square summable potentials, Comm. Math. Phys. 203 (1999), no. 2, 341-347.
    • (1999) Comm. Math. Phys. , vol.203 , Issue.2 , pp. 341-347
    • Deift, P.1    Killip, R.2
  • 10
    • 0011012701 scopus 로고
    • On the decoupling of finite singularities from the question of asymptotic completeness in two body quantum systems
    • P. Deift and B. Simon, On the decoupling of finite singularities from the question of asymptotic completeness in two body quantum systems, J. Functional Analysis 23 (1976), no. 3, 218-238.
    • (1976) J. Functional Analysis , vol.23 , Issue.3 , pp. 218-238
    • Deift, P.1    Simon, B.2
  • 11
    • 0001067228 scopus 로고
    • Appearance of a purely singular continuous spectrum in a class of random Schrödinger operators
    • F. Delyon, Appearance of a purely singular continuous spectrum in a class of random Schrödinger operators, J. Statist. Phys. 40 (1985), no. 5-6, 621-630.
    • (1985) J. Statist. Phys. , vol.40 , Issue.5-6 , pp. 621-630
    • Delyon, F.1
  • 12
    • 0001180136 scopus 로고
    • From power pure point to continuous spectrum in disordered systems
    • F. Delyon, B. Simon, and B. Souillard, From power pure point to continuous spectrum in disordered systems, Ann. Inst. H. Poincaré Phys. Théor. 42 (1985), no. 3, 283-309.
    • (1985) Ann. Inst. H. Poincaré Phys. Théor. , vol.42 , Issue.3 , pp. 283-309
    • Delyon, F.1    Simon, B.2    Souillard, B.3
  • 13
    • 0035457553 scopus 로고    scopus 로고
    • On the application of some of M.G. Krein's results to the spectral analysis of Sturm-Liouville operators
    • S.A. Denisov, On the application of some of M.G. Krein's results to the spectral analysis of Sturm-Liouville operators, J. Math. Anal. Appl. 261 (2001), no. 1, 177-191.
    • (2001) J. Math. Anal. Appl. , vol.261 , Issue.1 , pp. 177-191
    • Denisov, S.A.1
  • 17
    • 0002280835 scopus 로고
    • On subordinacy and analysis of the spectrum of one-dimensional Schrödinger operators
    • D.J. Gilbert and D.B. Pearson, On subordinacy and analysis of the spectrum of one-dimensional Schrödinger operators, J. Math. Anal. Appl. 128 (1987), no. 1, 30-56.
    • (1987) J. Math. Anal. Appl. , vol.128 , Issue.1 , pp. 30-56
    • Gilbert, D.J.1    Pearson, D.B.2
  • 19
    • 0001666109 scopus 로고    scopus 로고
    • Power-law subordinacy and singular spectra. I: Half-line operators
    • S. Jitomirskaya and Y. Last, Power-law subordinacy and singular spectra. I. Half-line operators, Acta Math. 183 (1999), no. 2, 171-189.
    • (1999) Acta Math. , vol.183 , Issue.2 , pp. 171-189
    • Jitomirskaya, S.1    Last, Y.2
  • 20
    • 36149008635 scopus 로고
    • On the scattering of a particle by a static potential
    • R. Jost and A. Pais, On the scattering of a particle by a static potential, Physical Rev. (2) 82 (1951), no. 6, 840-851.
    • (1951) Physical Rev. (2) , vol.82 , Issue.6 , pp. 840-851
    • Jost, R.1    Pais, A.2
  • 23
    • 0040523358 scopus 로고    scopus 로고
    • Absolutely continuous spectrum of one-dimensional Schrödinger operators and Jacobi matrices with slowly decreasing potentials
    • A. Kiselev, Absolutely continuous spectrum of one-dimensional Schrödinger operators and Jacobi matrices with slowly decreasing potentials, Comm. Math. Phys. 179 (1996), no. 2, 377-400.
    • (1996) Comm. Math. Phys. , vol.179 , Issue.2 , pp. 377-400
    • Kiselev, A.1
  • 24
    • 0001282745 scopus 로고    scopus 로고
    • Stability of the absolutely continuous spectrum of the Schrödinger equation under slowly decaying perturbations and a.e. convergence of integral operators
    • _, Stability of the absolutely continuous spectrum of the Schrödinger equation under slowly decaying perturbations and a.e. convergence of integral operators, Duke Math. J. 94 (1998), no. 3, 619-646.
    • (1998) Duke Math. J. , vol.94 , Issue.3 , pp. 619-646
  • 27
    • 0002388738 scopus 로고    scopus 로고
    • Modified prüfer and EFGP transforms and the spectral analysis of one-dimensional Schrödinger operators
    • A. Kiselev, Y. Last, and B. Simon, Modified Prüfer and EFGP transforms and the spectral analysis of one-dimensional Schrödinger operators, Comm. Math. Phys. 194 (1998), no. 1, 1-45.
    • (1998) Comm. Math. Phys. , vol.194 , Issue.1 , pp. 1-45
    • Kiselev, A.1    Last, Y.2    Simon, B.3
  • 28
    • 0001261704 scopus 로고
    • One-dimensional Schrödinger operators with random decaying potentials
    • S. Kotani and N. Ushiroya, One-dimensional Schrödinger operators with random decaying potentials, Comm. Math. Phys. 115 (1988), no. 2,247-266.
    • (1988) Comm. Math. Phys. , vol.115 , Issue.2 , pp. 247-266
    • Kotani, S.1    Ushiroya, N.2
  • 29
    • 0011002766 scopus 로고    scopus 로고
    • private communication
    • O. Kovrijkine, private communication.
    • Kovrijkine, O.1
  • 31
    • 0035625687 scopus 로고    scopus 로고
    • First KdV integrals and absolutely continuous spectrum for 1-D Schrödinger operator
    • S. Molchanov, M. Novitskii, and B. Vainberg, First KdV integrals and absolutely continuous spectrum for 1-D Schrödinger operator, Comm. Math. Phys. 216 (2001), no. 1, 195-213.
    • (2001) Comm. Math. Phys. , vol.216 , Issue.1 , pp. 195-213
    • Molchanov, S.1    Novitskii, M.2    Vainberg, B.3
  • 32
    • 0001062332 scopus 로고
    • On the dense point spectrum of Schrödinger and Dirac operators
    • S.N. Naboko, On the dense point spectrum of Schrödinger and Dirac operators, Teoret. Mat. Fiz. 68 (1986), no. 1, 18-28.
    • (1986) Teoret. Mat. Fiz. , vol.68 , Issue.1 , pp. 18-28
    • Naboko, S.N.1
  • 34
    • 0002464911 scopus 로고
    • Singular continuous measures in scattering theory
    • D.B. Pearson, Singular continuous measures in scattering theory, Comm. Math. Phys. 60 (1978), no. 1, 13-36.
    • (1978) Comm. Math. Phys. , vol.60 , Issue.1 , pp. 13-36
    • Pearson, D.B.1
  • 35
    • 0040516846 scopus 로고    scopus 로고
    • A probabilistic approach to one-dimensional Schrödinger operators with sparse potentials
    • C. Remling, A probabilistic approach to one-dimensional Schrödinger operators with sparse potentials, Comm. Math. Phys. 185 (1997), no. 2, 313-323.
    • (1997) Comm. Math. Phys. , vol.185 , Issue.2 , pp. 313-323
    • Remling, C.1
  • 36
    • 0032367056 scopus 로고    scopus 로고
    • The absolutely continuous spectrum of one-dimensional Schrödinger operators with decaying potentials
    • _, The absolutely continuous spectrum of one-dimensional Schrödinger operators with decaying potentials, Comm. Math. Phys. 193 (1998), no. 1, 151-170.
    • (1998) Comm. Math. Phys. , vol.193 , Issue.1 , pp. 151-170
  • 37
    • 22844454912 scopus 로고    scopus 로고
    • Bounds on embedded singular spectrum for one-dimensional Schrödinger operators
    • _, Bounds on embedded singular spectrum for one-dimensional Schrödinger operators, Proc. Amer. Math. Soc. 128 (2000), no. 1, 161-171.
    • (2000) Proc. Amer. Math. Soc. , vol.128 , Issue.1 , pp. 161-171
  • 38
    • 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, vol. 35, Cambridge University Press, Cambridge, 1979.
    • (1979) London Mathematical Society Lecture Note Series , vol.35
    • Simon, B.1
  • 39
    • 85016600983 scopus 로고
    • Schrödinger semigroups
    • _, Schrödinger semigroups, Bull. Amer. Math. Soc. (N.S.) 7 (1982), no. 3, 447-526.
    • (1982) Bull. Amer. Math. Soc. (N.S.) , vol.7 , Issue.3 , pp. 447-526
  • 40
    • 0000364033 scopus 로고
    • Some Jacobi matrices with decaying potential and dense point spectrum
    • _, Some Jacobi matrices with decaying potential and dense point spectrum, Comm. Math. Phys. 87 (1982/83), no. 2, 253-258.
    • (1982) Comm. Math. Phys. , vol.87 , Issue.2 , pp. 253-258
  • 41
    • 0001592725 scopus 로고
    • Operators with singular continuous spectrum. I. General operators
    • _, Operators with singular continuous spectrum. I. General operators, Ann. of Math. (2) 141 (1995), no. 1, 131-145.
    • (1995) Ann. of Math. (2) , vol.141 , Issue.1 , pp. 131-145
  • 42
    • 21444433761 scopus 로고    scopus 로고
    • Bounded eigenfunctions and absolutely continuous spectra for one-dimensional Schrödinger operators
    • _, Bounded eigenfunctions and absolutely continuous spectra for one-dimensional Schrödinger operators, Proc. Amer. Math. Soc. 124 (1996), no. 11, 3361-3369.
    • (1996) Proc. Amer. Math. Soc. , vol.124 , Issue.11 , pp. 3361-3369
  • 43
    • 21444440696 scopus 로고    scopus 로고
    • Some Schrödinger operators with dense point spectrum
    • _, Some Schrödinger operators with dense point spectrum, Proc. Amer. Math. Soc. 125 (1997), no. 1, 203-208.
    • (1997) Proc. Amer. Math. Soc. , vol.125 , Issue.1 , pp. 203-208
  • 44
    • 84961494757 scopus 로고
    • On the absolutely continuous spectrum of perturbed Sturm-Liouville operators
    • G. Stolz, On the absolutely continuous spectrum of perturbed Sturm-Liouville operators, J. reine angew. Math. 416 (1991), 1-23.
    • (1991) J. reine angew. Math. , vol.416 , pp. 1-23
    • Stolz, G.1
  • 46
    • 0002260691 scopus 로고
    • Spectral theory of ordinary differential operators
    • Springer-Verlag, Berlin
    • J. Weidmann, Spectral Theory of Ordinary Differential Operators, Lecture Notes in Mathematics, vol. 1258, Springer-Verlag, Berlin, 1987.
    • (1987) Lecture Notes in Mathematics , vol.1258
    • Weidmann, J.1


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