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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
Published electronically: September 22, 2003
MathSciNet review: 2022708
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Abstract: We consider discrete Schrödinger operators $H = \Delta + V$ in $\ell^2(\mathbb{Z} ^d)$with $d \ge 1$, and study the eigenvalue problem for these operators. It is shown that the point spectrum is empty if the potential $V$ is sufficiently well approximated by periodic potentials. This criterion is applied to quasiperiodic $V$ 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: http://dx.doi.org/10.1090/S0002-9947-03-03442-1
PII: S 0002-9947(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