Inhomogeneous Hilbert Boundary-Value Problem with a Finite Number of Second-Type Singularity Points

In this paper, we describe the inhomogeneous Hilbert boundary-value problem of the theory of analytic functions with an infinite index and a boundary condition for a half-plane. The coefficients of the boundary condition are Hölder-continuous everywhere except for a finite number of singular points...

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Vydané v:Journal of mathematical sciences (New York, N.Y.) Ročník 252; číslo 3; s. 436 - 444
Hlavní autori: Fatykhov, A. Kh, Shabalin, P. L.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Springer US 01.01.2021
Springer
Springer Nature B.V
Predmet:
Analytic functions
Boundary conditions
Boundary value problems
Complex variables
Entire functions
Mathematical analysis
Mathematics
Mathematics and Statistics
Singularity (mathematics)
entire functions
infinite index
35Q15
Phragmén–Lindelöf principle
Hilbert problem
30E25
ISSN:1072-3374, 1573-8795
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Popis
Shrnutí:In this paper, we describe the inhomogeneous Hilbert boundary-value problem of the theory of analytic functions with an infinite index and a boundary condition for a half-plane. The coefficients of the boundary condition are Hölder-continuous everywhere except for a finite number of singular points at which the argument of the coefficient function has second-type discontinuities (of a power order with exponent < 1). We obtain formulas for the general solution of the inhomogeneous problem and discuss the existence and uniqueness of the solution. The study is based on the theory of entire functions and the geometric theory of functions of a complex variable.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-020-05171-8