不可修正平曲线上的广义积分和边界值问题

IF 0.5 Q3 MATHEMATICS

Russian Mathematics Pub Date : 2024-02-28 DOI:10.3103/s1066369x23120046

D. B. Katz

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引用次数: 0

摘要

摘要本文讨论了两个密切相关的问题，即解决解析函数的黎曼边界值问题及其在具有不可修正边界的复平面域中的一些广义化问题，以及构建不可修正曲线上的曲线积分的广义化问题，该问题保留了对复分析非常重要的性质。这篇综述反映了该课题的现状，其中许多成果都是最新的。文末给出了一些尚未解决的问题，每个问题都可以作为科学研究的起点。

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Generalized Integration over Nonrectifiable Flat Curves and Boundary Value Problems

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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来源期刊

Russian Mathematics MATHEMATICS-

CiteScore

0.90

自引率

25.00%

发文量

期刊介绍： Russian Mathematics is a peer reviewed periodical that encompasses the most significant research in both pure and applied mathematics.