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Absence of Cantor spectrum for a class of Schrödinger operators
Author(s):
Norbert
Riedel
Journal:
Bull. Amer. Math. Soc.
29
(1993),
85-87.
MSC (2000):
Primary 47B39;
Secondary 34L40, 47E05, 47N50, 82B44
MathSciNet review:
1199856
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Additional information
Abstract:
It is shown that the complete localization of eigenvectors for the almost Mathieu operator entails the absence of Cantor spectrum for this operator.
References:
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- [1]
- J. Bellissard and B. Simon, Cantor spectrum for the almost Mathieu equation, J. Funct. Anal. 48 (1982), 408-519. MR 678179 (84h:81019)
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- M.-D. Choi, G. A. Elliott, and N. Yui, Gauss polynomials and the rotation algebra, Invent. Math. 99 (1990), 225-246. MR 1031901 (91b:46067)
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- N. Riedel, Almost Mathieu operators and rotation
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- -, The spectrum of a class of almost periodic operators, preprint.
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- B. Simon, Almost periodic Schrödinger operators: a review, Adv. in Appl. Math. 3 (1982), 463-490. MR 682631 (85d:34030)
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- Ya. G. Sinai, Anderson localization for one-dimensional difference Schrödinger operator with quasiperiodic potential, J. Stat. Phys. 46 (1987), 861-909. MR 893122 (88h:82016)
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Additional Information:
DOI:
10.1090/S0273-0979-1993-00406-3
PII:
S 0273-0979(1993)00406-3
Copyright of article:
Copyright
1993,
American Mathematical Society
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