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arXiv · 1702.00965

Asymptotic Eigenfunctions for a class of Difference Operators

Markus Klein·Elke Rosenberger
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Abstract

We analyze a general class of difference operators $H_\varepsilon = T_\varepsilon + V_\varepsilon$ on $\ell^2(\varepsilon \mathbb{Z}^d)$, where $V_\varepsilon$ is a one-well potential and $\varepsilon$ is a small parameter. We construct formal asymptotic expansions of WKB-type for eigenfunctions associated with the low lying eigenvalues of $H_\varepsilon$. These are obtained from eigenfunctions or quasimodes for the operator $H_\varepsilon$, acting on $L^2(\mathbb{R}^d)$, via restriction to the lattice $\varepsilon\mathbb{Z}^d$.

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Markus Klein, Elke Rosenberger. 2017-02-03. Asymptotic Eigenfunctions for a class of Difference Operators. https://doi.org/10.3233/asy-2010-1025

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