Аннотация:
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.
Ключевые слова:
Riemann–Hilbert problem, maximum principle, infinite index, entire functions.
Образец цитирования:
A. Kh. Fatykhov, P. L. Shabalin, “Solvability homogeneous Riemann–Hilbert boundary value problem with several points of turbulence”, Пробл. анал. Issues Anal., 7(25), спецвыпуск (2018), 31–39
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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 Пробл. анал. Issues Anal.
\yr 2018
\vol 7(25)
\pages 31--39
\issueinfo спецвыпуск
\mathnet{http://mi.mathnet.ru/pa240}
\crossref{https://doi.org/10.15393/j3.art.2018.5530}
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Эта публикация цитируется в следующих 4 статьяx:
Anis Galimyanov, Tatyana Gorskaya, E. Vdovin, “Calculation of fractional integrals using partial sums of Fourier series for structural mechanics problems”, E3S Web Conf., 274 (2021), 03011
Juan Bory-Reyes, “A note on the solvability of homogeneous Riemann boundary problem with infinity index”, Communications in Mathematics, 29:3 (2021), 527
П. Л. Шабалин, А. Х. Фатыхов, “Неоднородная краевая задача Гильберта с конечным числом точек завихрения логарифмического порядка”, Изв. вузов. Матем., 2021, № 1, 64–80; P. L. Shabalin, A. Kh. Fatykhov, “Inhomogeneous Hilbert boundary value problem with several points of logarithmic turbulence”, Russian Math. (Iz. VUZ), 65:1 (2021), 57–71
Pavel Shabalin, Rafael Faizov, E. Vdovin, “Hilbert boundary value problem for generalized analytic functions with a singular line”, E3S Web Conf., 274 (2021), 11003
Цитирование в формате AMSBIB
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