E. B. Afanas’eva, V. B. Vasil’ev, A. B. Kamanda Bongay
{"title":"Discrete Equations, Discrete Transformations, and Discrete Boundary Value Problems","authors":"E. B. Afanas’eva, V. B. Vasil’ev, A. B. Kamanda Bongay","doi":"10.1134/s0012266123120108","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We study the solvability of discrete elliptic pseudodifferential equations in a sector of the\nplane. Using special factorization of the symbol, the problem is reduced to a boundary value\nproblem for analytic functions of two variables. A periodic analog of one integral transformation is\nobtained that was used to construct solutions of elliptic pseudodifferential equations in conical\ndomains. The formula for the general solution of the discrete equation under consideration and\nsome boundary value problems are described in terms of this transformation.\n</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0012266123120108","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We study the solvability of discrete elliptic pseudodifferential equations in a sector of the
plane. Using special factorization of the symbol, the problem is reduced to a boundary value
problem for analytic functions of two variables. A periodic analog of one integral transformation is
obtained that was used to construct solutions of elliptic pseudodifferential equations in conical
domains. The formula for the general solution of the discrete equation under consideration and
some boundary value problems are described in terms of this transformation.