Stability of singular spectral types under decaying pertubations

Journal of Functional Analysis

Volumn 198, Issue 1, 2003, Pages 1-27

  Kiselev, Alexander ^a   Last, Yoram ^b   Simon, Barry ^c  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

^b HEBREW UNIVERSITY OF JERUSALEM   (Israel)

^c CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037455848     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-1236(02)00053-8     Document Type: Article

References (21)

1. J. Berezanskii, Expansions in Eigenfunctions of Selfadjoint Operators, in: Translation of Mathematical Monographs, Vol. 17, Amer. math. Soc., Providence, RI, 1968.
2. M. Christ, A. Kiselev, W K B and spectral analysis of one-dimensional Schrödinger operators with slowly varying potentials, Comm. Math. Phys. 218 (2001) 245-262.
3. E.A. Coddington, N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill, New York, 1955.
4. P. Deift, R. Killip, On the absolutely continuous spectrum of one-dimensional Schrödinger operators with square summable potentials, Comm. Math. Phys. 203 (1999) 341-347.
5. R. del Rio, B. Simon, G. Stolz, Stability of spectral types for Sturm-Liouville operators, Math. Res. Lett. 1 (1994) 437-450.
6. M.S.P. Eastham, The Asymptotic Solution of Linear Differential Systems, Clarendon Press Oxford, 1989.
7. D.J. Gilbert, D.B. Pearson, On subordinacy and analysis of the spectrum of one-dimensional Schrödinger operators, J. Math. Anal. Appl. 128 (1987) 30-56.
8. P. Hartman, Ordinary Differential Equations, Wiley, New York, 1964.
9. S. Jitomirskaya, Y. Last, Power-law subordinacy and singular spectra, I. Half-line operators, Acta Math. 183 (1999) 171-189.
10. R. Killip, Perturbations of one-dimensional Schrödinger operators preserving the absolutely continuous spectrum, Int. Math. Res. Not. 38 (2002) 2029-2061.
11. A. Kiselev, Y. Last, B. Simon, Modified Prüfer and EFGP transforms and deterministics models with dense point spectrum, J. Funct. Anal. 154 (1998) 513-530.
12. Y. Last, Quantum dynamics and decomposition of singular continuous spaces, J. Funct. Anal. 142 (1996) 406-445.
13. N. Levinson, The asymptotic nature of the solutions of linear systems of differential equations, Duke Math. J. 15 (1948) 111-126.
14. M. Reed, B. Simon, Methods of Modern Mathematical Physics, I. Functional Analysis, Academic Press, London, San Diego, 1980.
15. M. Reed, B. Simon, Methods of Modern Mathematical Physics, III. Scattering Theory, Academic Press, London, San Diego, 1979.
16. C.A. Rogers, S.J. Taylor, The analysis of additive set functions in Euclidean space, Acta Math. 101 (1959) 273-302.
17. C.A. Rogers, S.J. Taylor, Additive set functions in Euclidean space, II, Acta Math. 109 (1963) 207-240.
18. D. Ruelle, Ergodic theory of differentiable dynamical systems, Publ. Math. IHES 50 (1979) 275-306.
19. B. Simon, Schrödinger semigroups, Bull. Amer. Math. Soc. 7 (1982) 447-526.
20. B. Simon, Spectral analysis of rank one perturbations and applications, in: J. Feldman, R. Froese, L. Rosen (Eds.), CRM Proceedings and Lecture Notes, Vol. 8, Amer. Math. Soc., Providence, RI, 1995, pp. 109-149.
21. B. Simon, Bounded eigenfunctions and absolutely continuous spectra for one-dimensional Schrödinger operators, Proc. Amer. Math. Soc. 124 (1996) 3361-3369.