Transactions of the American Mathematical Society

Author(s): David Damanik
Journal: Trans. Amer. Math. Soc. 356 (2004), 495-507.
MSC (2000): Primary 81Q10, 47B39
Posted: September 22, 2003
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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

is sufficiently well approximated by periodic potentials. This criterion is applied to quasiperiodic

and to so-called Fibonacci-type superlattices.

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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 81Q10, 47B39

David Damanik
Affiliation: Department of Mathematics 253--37, California Institute of Technology, Pasadena, California 91125
Email: damanik@its.caltech.edu

DOI: 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
Posted: September 22, 2003
Additional Notes: This research was partially supported by NSF grant DMS--0010101
Copyright of article: Copyright 2003, American Mathematical Society

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