{"title":"Trajectory Symbols and the Fredholm Property of Boundary Value Problems for Differential Operators with Shifts","authors":"A. V. Boltachev, A. Yu. Savin","doi":"10.1134/S1061920823020012","DOIUrl":null,"url":null,"abstract":"<p> Boundary value problems are considered in which the main operator and the operators of boundary conditions include differential and shift operators corresponding to the action of a discrete group. The manifold on which the boundary value problem is considered is not assumed to be group invariant. A definition of trajectory symbols for this class of boundary value problems is given. It is shown that elliptic problems define Fredholm operators in the corresponding Sobolev spaces. An application to problems with extensions and contractions is given. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 2","pages":"135 - 151"},"PeriodicalIF":1.7000,"publicationDate":"2023-06-18","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/S1061920823020012","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
Boundary value problems are considered in which the main operator and the operators of boundary conditions include differential and shift operators corresponding to the action of a discrete group. The manifold on which the boundary value problem is considered is not assumed to be group invariant. A definition of trajectory symbols for this class of boundary value problems is given. It is shown that elliptic problems define Fredholm operators in the corresponding Sobolev spaces. An application to problems with extensions and contractions is given.
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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