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Published 2004 | Published
Journal Article Open

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

Abstract

We consider discrete Schrödinger operators in H = Δ + V in ℓ^2(Z^d) with d ≥ 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.

Additional Information

© 2003 American Mathematical Society. Received by the editors October 9, 2001. Article electronically published on September 22, 2003. This research was partially supported by NSF grant DMS-0010101.

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August 19, 2023
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