Modified Prüfer and EFGP Transforms and Deterministic Models with Dense Point Spectrum

Journal of Functional Analysis

Volumn 154, Issue 2, 1998, Pages 513-530

  Last, Yoram ^a   Simon, Barry ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000421261     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.1997.3192     Document Type: Article

References (18)

1. Behncke H. Absolute continuity of Hamiltonians with von Neumann-Wigner potentials, II. Manuscripta Math. 71:1991;163-181.
2. Birkhoff G., Rota G. C. Ordinary Differential Equations. 1978;Wiley, New York.
3. del Rio R., Makarov N., Simon B. Operators with singular continuous spectrum, II. Rank one operators. Comm. Math. Phys. 165:1994;59-67.
4. del Rio R., Simon B., Stolz G. Stability of spectral types for Sturm-Liouville operators. Math. Research Lett. 1:1994;437-450.
5. Eggarter T. Some exact results on electron energy levels in certain one-dimensional random potentials. Phys. Rev. B. 5:1972;3863-3865.
6. Gordon A. Ya. Deterministic potential with a pure point spectrum. Math. Notes. 48:1990;1197-1203.
7. Gordon A. Pure point spectrum under 1-parameter perturbations and instability of Anderson localization. Comm. Math. Phys. 164:1994;489-505.
8. Gredeskul S. A., Pastur L. A. Behavior of the density of states in one-dimensional disordered systems near the edges of the spectrum. Theoret. and Math. Phys. 23:1975;132-139.
9. Kirsch W., Molchanov S. A., Pastur L. A. One-dimensional Schrödinger operator with high potential barriers. Oper. Theory Adv. Appl. 57:1992;163-170.
10. A. Kiselev, Y. Last, B. Simon, Modified Prüfer and EFGP transforms and the spectral analysis of one-dimensional Schrödinger operators, Comm. Math. Phys.
11. Y. Last, B. Simon, Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrödinger operators.
12. Pastur L., Figotin A. Spectra of Random and Almost-Periodic Operators. 1992;Springer-Verlag, Berlin/New York.
13. Ruelle D. Ergodic theory of differentiable dynamical systems. Publ. Math. IHES. 50:1979;275-306.
14. Simon B. Spectral analysis and rank one perturbations and applications. CRM Lecture Notes. 1995;Amer. Math. Soc. Providence. p. 109-149.
15. Simon B., Spencer T. Trace class perturbations and the absence of absolutely continuous spectrum. Comm. Math. Phys. 125:189;113-126.
16. Simon B., Wolff T. Singular continuous spectrum under rank one perturbations and localization for random Hamiltonians. Comm. Pure Appl. Math. 39:1986;75-90.
17. Simon B., Zhu Y. F. The Lyapunov exponents for Schrödinger operators with slowly oscillating potentials. J. Funct. Anal. 140:1996;541-556.
18. Stolz G. Bounded solutions and absolute continuity of Sturm-Liouville operators. J. Math. Anal. Appl. 169:1992;210-228.