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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, Number 1, Pages 64–80
DOI: https://doi.org/10.26907/0021-3446-2021-1-64-80 (Mi ivm9641) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Inhomogeneous Hilbert boundary value problem with several points of logarithmic turbulence

P. L. Shabalin, A. Kh. Fatykhov

Kazan State Architecture and Civil Engineering University, 1 Zelyonaya str., Kazan, 420043 Russia
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DOI: https://doi.org/10.26907/0021-3446-2021-1-64-80
Abstract: We consider the so called Hilbert boundary value problem with boundary condition in the unit disk. Its coficient is assumed to be Hölder-continuous everywhere on the unit circle excluding a finite set of points. At these points its argument has nonremovable discontinuity of logarithmic order. We obtain formulas for the general solution and describe completely the solvability picture in a class of analytic and bounded functions in unit disc. Our technique is based on the theory of entire functions of zero-order approximation and the geometric theory of functions. The results obtained are applied to the study of the solvability of a single boundary value problem for a certain class generalized analytic function.
Keywords: Riemann–Hilbert problem, maximum principle, infinite index, entire functions of zero-order approximation, generalized analytic function.
Received: 09.03.2020
Revised: 24.06.2020
Accepted: 29.06.2020
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2021, Volume 65, Issue 1, Pages 57–71
DOI: https://doi.org/10.3103/S1066369X21010059
Bibliographic databases:
Document Type: Article
UDC: 517.544
Language: Russian
Citation: P. L. Shabalin, A. Kh. Fatykhov, “Inhomogeneous Hilbert boundary value problem with several points of logarithmic turbulence”, Izv. Vyssh. Uchebn. Zaved. Mat., 2021, no. 1, 64–80; Russian Math. (Iz. VUZ), 65:1 (2021), 57–71
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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