一类差分算子的渐近特征函数

Asymptot. Anal. Pub Date : 2017-02-03 DOI:10.3233/ASY-2010-1025

M. Klein, Elke Rosenberger

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引用次数: 13

摘要

我们分析了一类一般的差分算子He = Te + Ve on 2 ((eZ) d)，其中Ve是单井势，e是一个小参数。构造了与He的低特征值相关的特征函数的wkb型渐近展开式。这些是通过对晶格(eZ) d的限制，从作用于l2 (rd)的算子He的本征函数或准模中得到的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Asymptotic eigenfunctions for a class of difference operators

We analyze a general class of difference operators He = Te + Ve on � 2 ((eZ) d ), where Ve is a one-well potential and e is a small parameter. We construct formal asymptotic expansions of WKB-type for eigenfunctions associated with the low lying eigenvalues of He. These are obtained from eigenfunctions or quasimodes for the operator He, acting on L 2 (R d ), via restriction to the lattice (eZ) d .

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Asymptot. Anal.

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