A version of Gordon's theorem for multi-dimensional Schrödinger operators

Author:
David Damanik

Journal:
Trans. Amer. Math. Soc. **356** (2004), 495-507

MSC (2000):
Primary 81Q10, 47B39

DOI:
https://doi.org/10.1090/S0002-9947-03-03442-1

Published electronically:
September 22, 2003

MathSciNet review:
2022708

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Abstract | References | Similar Articles | Additional Information

Abstract: We consider discrete Schrödinger operators in with , and study the eigenvalue problem for these operators. It is shown that the point spectrum is empty if the potential is sufficiently well approximated by periodic potentials. This criterion is applied to quasiperiodic and to so-called Fibonacci-type superlattices.

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Additional Information

**David Damanik**

Affiliation:
Department of Mathematics 253–37, California Institute of Technology, Pasadena, California 91125

Email:
damanik@its.caltech.edu

DOI:
https://doi.org/10.1090/S0002-9947-03-03442-1

Keywords:
Schr\"odinger operators,
absence of eigenvalues,
quasiperiodic potentials

Received by editor(s):
October 9, 2001

Published electronically:
September 22, 2003

Additional Notes:
This research was partially supported by NSF grant DMS–0010101

Article copyright:
© Copyright 2003
American Mathematical Society