The Riemann problem on a ray 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, 1 Zelenaya St, Kazan 420043, Russia

来源：

IZVESTIYA OF SARATOV UNIVERSITY MATHEMATICS MECHANICS INFORMATICS | 2023年 / 23卷 / 01期

关键词：

Riemann problem; generalized analytical functions; infinite index; integer functions of refined zero order; BOUNDARY-VALUE PROBLEM; INTEGRAL-REPRESENTATIONS; SYSTEM; EQUATION;

D O I：

10.18500/1816-9791-2023-23-1-58-69

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study an inhomogeneous Riemann boundary value problem with a finite index and a boundary condition on a ray for a generalized Cauchy - Riemann equation with a singular coefficient. For the solution of this problem, we derived a formula for the general solution of the generalized Cauchy - Riemann equation under constraints that led to an infinite index of logarithmic order of the accompanying problem for analytical functions. We have obtained a formula for the general solution of the Riemann problem and conducted a complete study of the existence and the number of solutions of a boundary value problem for generalized analytic functions with a singular line.

引用

页码：58 / 69

页数：12

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