The Riemann Problem in a Half-Plane for Generalized Analytic Functions with a Singular Line

被引：1

作者：

Shabalin, P. L. ^{[1
]}

Faizov, R. R. ^{[1
]}

机构：

[1] Kazan State Univ Architecture & Engn, Kazan 420043, Russia

来源：

RUSSIAN MATHEMATICS | 2023年 / 67卷 / 03期

关键词：

Riemann problem; generalized analytic function; infinite index; entire function of given order zero; BOUNDARY-VALUE PROBLEM; EQUATION; SYSTEM;

D O I：

10.3103/S1066369X23030052

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we have studied an inhomogeneous Riemann boundary value problem with a finite index and a boundary condition on the real axis for one generalized Cauchy-Riemann equation with singular coefficients. To solve this problem, we derived a structural formula for the general solution to the generalized equation and conducted a complete study of the solvability of the Riemann boundary value problem of the theory of analytic functions with an infinite index of logarithmic order. Based on the results of this study, we derived a formula for a general solution and studied the existence and the number of solutions to boundary value problems for generalized analytical functions.

引用

页码：66 / 75

页数：10

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