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Sibirskii Matematicheskii Zhurnal, 2015, Volume 56, Number 1, Pages 13–26 (Mi smj2618)  
This article is cited in 1 scientific paper (total in 1 paper)

Explicit forms for the Schwarz integrals in an annulus and their applications

N. R. Abubakirova, L. A. Aksent'evb

a Lobachevskiĭ Institute of Mathematics and Mechanics, Kazan (Volga Region) Federal University, Kazan, Russia
b Lobachevskiĭ Institute of Mathematics and Mechanics, Kazan (Volga Region) Federal University, Kazan, Russia
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Abstract: The article presents new explicit forms of the Schwarz integral in an annulus. Some correspondence is obtained between the Fourier series for the boundary values of the Schwarz problem and the Laurent series for a regular function $f(z)$ that is the solution of the Schwarz problem. We study in detail the case of a linear-fractional function as a solution to the Schwarz problem in a disk, an annulus, and an arbitrary multiply-connected domain with an application to inverse boundary value problems.
Keywords: Schwarz integral, Fourier series, Laurent series, inverse boundary value problems.
Received: 11.02.2014
English version:
Siberian Mathematical Journal, 2015, Volume 56, Issue 1, Pages 9–20
DOI: https://doi.org/10.1134/S0037446615010024
Bibliographic databases:
Document Type: Article
UDC: 517.544
Language: Russian
Citation: N. R. Abubakirov, L. A. Aksent'ev, “Explicit forms for the Schwarz integrals in an annulus and their applications”, Sibirsk. Mat. Zh., 56:1 (2015), 13–26; Siberian Math. J., 56:1 (2015), 9–20
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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