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.
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页码：58 / 69
页数：12
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