Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


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Shabalin P. L., Faizov R. R. The Riemann problem on a ray for generalized analytic functions with a singular line. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2023, vol. 23, iss. 1, pp. 58-69. DOI: 10.18500/1816-9791-2023-23-1-58-69, EDN: UYQLJS

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
01.03.2023
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Russian
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Article
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517.54
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UYQLJS

The Riemann problem on a ray for generalized analytic functions with a singular line

Autors: 
Shabalin Pavel Leonidovich, Kazan State University of Architecture and Engineering
Faizov Rafael Rustamovich, Kazan State University
Abstract: 

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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Received: 
09.08.2022
Accepted: 
26.09.2022
Published: 
01.03.2023