{"title":"Explicit Solution to the Birman Problem for the 2D-Laplace Operator","authors":"M. Malamud","doi":"10.1134/S1061920824030117","DOIUrl":null,"url":null,"abstract":"<p> We construct an appropriate restriction of the 2-dimensional Laplace operator that has compact preresolvent though the resolvent of its Friedrichs extension is not compact and, moreover, its spectrum is absolutely continuous. This result solves the Birman problem. </p><p> <b> DOI</b> 10.1134/S1061920824030117 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 3","pages":"495 - 503"},"PeriodicalIF":1.7000,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Journal of Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S1061920824030117","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
We construct an appropriate restriction of the 2-dimensional Laplace operator that has compact preresolvent though the resolvent of its Friedrichs extension is not compact and, moreover, its spectrum is absolutely continuous. This result solves the Birman problem.
期刊介绍：
Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.
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