Measurable enumeration of eigenelements

Applicable Analysis

Volumn 71, Issue 1-4, 1998, Pages 41-61

  Gordon, Alexander Y ^a,c   Kechris, Alexander S ^b  

^a UNIVERSITY OF NORTH CAROLINA AT CHARLOTTE   (United States)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^c INSTITUTE OF EARTHQUAKE PREDICTION THEORY AND MATHEMATICAL GEOPHYSICS   (Russian Federation)

Author keywords

Eigenvalue; Eigenvector; Measurable enumeration; Measurable space

Indexed keywords

EID: 85070133437     PISSN: 00036811     EISSN: 1563504X     Source Type: Journal    
DOI: 10.1080/00036819908840704     Document Type: Article

References (12)

1. Carmona, R., and Lacroix, J., 1990. J. Spectral theory of random Schrödinger operators, Boston: Birkhäuser.
2. Cycon, H., Fröse, R., Kirsch, W., and Simon, B., 1987. Schrödinger operators, Berlin, Heidelberg: Springer-Verlag.
3. Foöhilich, J., Spencer, T., and Wittwer, P., 1990. Localization for a class of one-dimensional quasi-periodic Schrödinger operators. Commun. Math. Phys, 132: 5–25.
4. Gordon, A. Y., Jitomirskaya, S., Last, Y., and Simon, B., 1997. Duality and singular continuous spectrum in the almost Mathieu equation. Acta Mathematica, 178: 169–183.
5. Jitomirskaya, S., 1994. Anderson localization for the almost Mathieu equation: a non-perturbative proof. Comm. Math. Phys, 165: 49–57.
6. Kalisch, G., 1972. On operators on separable Banach spaces with arbitrary prescribed point spectrum. Proc. Amer. Math. Soc, 34 (1): 207–208.
7. Kechris, A. S., Classical Descriptive Set Theory. Graduate Texts in Mathematics
8. Molchanov, S. A., 1978. The structure of eigenfunctions of one-dimensional disordered structures. Math. USSR lzv, 75: 69–101.
9. Moschovakis, Y. N., 1980. Descriptive Set Theory, North Holland.
10. Pastur, L., 1980. Spectral properties of disordered systems in one-body approximation. Comm. Math. Phys, 75: 179–196.
11. Pastur, L., and Figotin, A., 1992. Spectra of random and almost-periodic operators, Berlin, Heidelberg: Springer-Verlag.
12. Sinai and Ya, G., 1987. Anderson localization for one-dimensional difference Schrödinger operator with quasiperiodic coefficients. Comm. Math. Phys, 46: 861–909.