Sub-exponential decay of eigenfunctions for some discrete Schrödinger operators

  • Marc-Adrien Mandich

    Université de Bordeaux, Talence, France
Sub-exponential decay of eigenfunctions for some discrete Schrödinger operators cover
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Abstract

Following the method of Froese and Herbst, we show for a class of potentials that an embedded eigenfunction with eigenvalue of the multi-dimensional discrete Schrödinger operator on decays sub-exponentially whenever the Mourre estimate holds at . In the one-dimensional case we further show that this eigenfunction decays exponentially with a rate at least of cosh, where is the nearest threshold of located between and . A consequence of the latter result is the absence of eigenvalues between 2 and the nearest thresholds above and below this value. The method of Combes–Thomas is also reviewed for the discrete Schrödinger operators.

Cite this article

Marc-Adrien Mandich, Sub-exponential decay of eigenfunctions for some discrete Schrödinger operators. J. Spectr. Theory 9 (2019), no. 1, pp. 21–77

DOI 10.4171/JST/240