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

Damanik, David

doi:10.1090/S0002-9947-03-03442-1

A version of Gordon’s theorem for multi-dimensional Schrödinger operators
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by David Damanik

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

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

Published electronically: 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 $V$ 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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