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

共 38 条

[1] The Riemann Problem in a Half-Plane for Generalized Analytic Functions with a Singular Line
P. L. Shabalin
R. R. Faizov
Russian Mathematics, 2023, 67 : 66 - 75
[2] The Riemann problem on a ray for generalized analytic functions with a singular line
Shabalin, P. L.
Faizov, R. R.
IZVESTIYA OF SARATOV UNIVERSITY MATHEMATICS MECHANICS INFORMATICS, 2023, 23 (01): : 58 - 69
[3] The Hilbert Problem in a Half-Plane for Generalized Analytic Functions with a Singular Point on the Real Axis
Shabalin, P. L.
Faizov, R. R.
UCHENYE ZAPISKI KAZANSKOGO UNIVERSITETA-SERIYA FIZIKO-MATEMATICHESKIE NAUKI, 2024, 166 (01): : 111 - 122
[4] The Riemann Problem in a Half-Plane for Generalized Analytic Functions with a Supersingular Point on the Contour of the Boundary Condition
Shabalin, P. L.
RUSSIAN MATHEMATICS, 2023, 67 (11) : 85 - 89
[5] The Hilbert Problem in a Half-plane for Generalized Analytic Functions with a Super-singular Point on the Contour of the Boundary Condition
Shabalin, P. L.
Khasanova, E. N.
LOBACHEVSKII JOURNAL OF MATHEMATICS, 2023, 44 (12) : 5398 - 5405
[6] The Riemann Problem with a Condition on the Real Axis for Generalized Analytic Functions with a Singular Curve
Shabalin, P. L.
Faizov, R. R.
SIBERIAN MATHEMATICAL JOURNAL, 2023, 64 (02) : 431 - 442
[7] The Hilbert Problem in a Half-plane for Generalized Analytic Functions with a Super-singular Point on the Contour of the Boundary Condition
P. L. Shabalin
E. N. Khasanova
Lobachevskii Journal of Mathematics, 2023, 44 : 5398 - 5405
[8] The Riemann Problem with a Condition on the Real Axis for Generalized Analytic Functions with a Singular Curve
P. L. Shabalin
R. R. Faizov
Siberian Mathematical Journal, 2023, 64 : 431 - 442
[9] On a Riemann Boundary Value Problem in the Half-plane in the Class of Weighted Continuous Functions
H. M. Hayrapetyan
S. A. Aghekyan
Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences), 2019, 54 : 79 - 89
[10] On a Riemann Boundary Value Problem in the Half-plane in the Class of Weighted Continuous Functions
Hayrapetyan, H. M.
Aghekyan, S. A.
JOURNAL OF CONTEMPORARY MATHEMATICAL ANALYSIS-ARMENIAN ACADEMY OF SCIENCES, 2019, 54 (02): : 79 - 89

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