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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika
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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 4 scientific papers (total in 4 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
Full-text PDF (413 kB) Citations (4)
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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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\jour Izv. Vyssh. Uchebn. Zaved. Mat.
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\pages 64--80
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\issue 1
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Linking options:
  • https://www.mathnet.ru/eng/ivm9641
  • https://www.mathnet.ru/eng/ivm/y2021/i1/p64
  • This publication is cited in the following 4 articles:
    1. P. L. Shabalin, R. R. Faizov, “The Hilbert problem in a half-plane for generalized analytic functions with a singular point on the real axis”, jour, 166:1 (2024), 111  crossref
    2. A. Darya, N. Tagkhizadekh, “Zadachi Shvartsa i Dirikhle dlya ˉ-uravneniya v treugolnoi oblasti”, Izv. vuzov. Matem., 2024, no. 11, 12–22  mathnet  crossref
    3. Pavel Shabalin, Rafael Faizov, E. Vdovin, “Hilbert boundary value problem for generalized analytic functions with a singular line”, E3S Web Conf., 274 (2021), 11003  crossref
    4. Nail Tuktamyshov, E. Vdovin, “Explosive technologies in transport construction”, E3S Web Conf., 274 (2021), 02002  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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