{"title":"Asymptotic eigenfunctions for a class of difference operators","authors":"M. Klein, Elke Rosenberger","doi":"10.3233/ASY-2010-1025","DOIUrl":null,"url":null,"abstract":"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 .","PeriodicalId":8603,"journal":{"name":"Asymptot. Anal.","volume":"18 1","pages":"1-36"},"PeriodicalIF":0.0000,"publicationDate":"2017-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"13","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Asymptot. Anal.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3233/ASY-2010-1025","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 13
Abstract
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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