{"title":"Generalized Integration over Nonrectifiable Flat Curves and Boundary Value Problems","authors":"D. B. Katz","doi":"10.3103/s1066369x23120046","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Two closely related problems are discussed, viz., solving the Riemann boundary value problem for analytic functions and some of their generalizations in the domains of the complex plane with nonrectifiable boundaries and constructing a generalization of the curvilinear integral onto nonrectifiable curves that preserves the properties important for the complex analysis. This review reflects the current state of the topic, with many of the results being quite recent. At the end of the work, a number of unsolved problems are given, each of which can serve as a starting point for scientific research.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":"7 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-02-28","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/s1066369x23120046","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Two closely related problems are discussed, viz., solving the Riemann boundary value problem for analytic functions and some of their generalizations in the domains of the complex plane with nonrectifiable boundaries and constructing a generalization of the curvilinear integral onto nonrectifiable curves that preserves the properties important for the complex analysis. This review reflects the current state of the topic, with many of the results being quite recent. At the end of the work, a number of unsolved problems are given, each of which can serve as a starting point for scientific research.
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