{"title":"The Riemann Problem in a Half-Plane for Generalized Analytic Functions with a Supersingular Point on the Contour of the Boundary Condition","authors":"P. L. Shabalin","doi":"10.3103/s1066369x23110075","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, we study an inhomogeneous Riemann boundary value problem with a finite index and a boundary condition on the real axis for a generalized Cauchy–Riemann equation with supersingular coefficients. To solve the problem, it was necessary to derive a structural formula for the general solution to this equation and to investigate the solvability of the Riemann boundary value problem of the theory of analytic functions with an infinite index due to the power-order vorticity point.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":"13 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3103/s1066369x23110075","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
In this paper, we study an inhomogeneous Riemann boundary value problem with a finite index and a boundary condition on the real axis for a generalized Cauchy–Riemann equation with supersingular coefficients. To solve the problem, it was necessary to derive a structural formula for the general solution to this equation and to investigate the solvability of the Riemann boundary value problem of the theory of analytic functions with an infinite index due to the power-order vorticity point.
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