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Probl. Anal. Issues Anal., 2018, Volume 7(25), special issue, Pages 31–39 (Mi pa240)  

Solvability homogeneous Riemann–Hilbert boundary value problem with several points of turbulence

A. Kh. Fatykhov, P. L. Shabalin

Kazan State University of Architecture and Engineering, Kazan, Russia

Abstract: We consider the so called Hilbert boundary value problem with infinite index in the unit disk. Its coefficient is assumed to be Hölder-continuous everywhere on the unit circle excluding a finite set of points. At these points its argument has power discontinuities of orders less than one. We obtain formulas for the general solution and describe completely the solvability picture in a special functional class. Our technique is based on the theory of entire functions and the geometric theory of functions.

Keywords: Riemann–Hilbert problem, maximum principle, infinite index, entire functions.

Funding Agency Grant Number
Russian Foundation for Basic Research 17-01-00282_a
This work was supported by RFFI (project 17-01-00282-a).


DOI: https://doi.org/10.15393/j3.art.2018.5530

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UDC: 517.54
MSC: 30E25
Received: 10.06.2018
Revised: 19.09.2018
Accepted:17.09.2018
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Citation: A. Kh. Fatykhov, P. L. Shabalin, “Solvability homogeneous Riemann–Hilbert boundary value problem with several points of turbulence”, Probl. Anal. Issues Anal., 7(25), special issue (2018), 31–39

Citation in format AMSBIB
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\by A.~Kh.~Fatykhov, P.~L.~Shabalin
\paper Solvability homogeneous Riemann--Hilbert boundary value problem with several points of turbulence
\jour Probl. Anal. Issues Anal.
\yr 2018
\vol 7(25)
\pages 31--39
\issueinfo special issue
\mathnet{http://mi.mathnet.ru/pa240}
\crossref{https://doi.org/10.15393/j3.art.2018.5530}
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