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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2022, Volume 503, Pages 76–82
DOI: https://doi.org/10.31857/S2686954322020163 (Mi danma254) 		 
This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

Singular integral operators with a generalized Cauchy kernel

A. P. Soldatovabcd

a Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, Moscow, Russia
b Moscow Center for Fundamental and Applied Mathematics
c National Research University "Moscow Power Engineering Institute"
d Academy of Science of the Republic of Sakha (Yakutia)
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DOI: https://doi.org/10.31857/S2686954322020163
Abstract: Singular integral operators with piecewise continuous matrix coefficients are considered on a piecewise smooth curve in weighted Lebesgue spaces. In contrast to the classical case, the operators have generalized Cauchy kernels arising as a parametrix of first-order elliptic systems in the plane. A Fredholmness criterion and an index formula for these operators are obtained in weighted Lebesgue spaces.
Keywords: singular integral operators, piecewise Lyapunov curve, generalized Cauchy kernels, Fredholm property, index formula, weighted Lebesgue spaces, first-order elliptic systems.
Presented: E. I. Moiseev
Received: 02.03.2021
Revised: 02.03.2021
Accepted: 04.02.2022
English version:
Doklady Mathematics, 2022, Volume 105, Issue 2, Pages 117–122
DOI: https://doi.org/10.1134/S1064562422020168
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: A. P. Soldatov, “Singular integral operators with a generalized Cauchy kernel”, Dokl. RAN. Math. Inf. Proc. Upr., 503 (2022), 76–82; Dokl. Math., 105:2 (2022), 117–122
Citation in format AMSBIB
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\by A.~P.~Soldatov
\paper Singular integral operators with a generalized Cauchy kernel
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2022
\vol 503
\pages 76--82
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\crossref{https://doi.org/10.31857/S2686954322020163}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4448480}
\elib{https://elibrary.ru/item.asp?id=48506208}
\transl
\jour Dokl. Math.
\yr 2022
\vol 105
\issue 2
\pages 117--122
\crossref{https://doi.org/10.1134/S1064562422020168}
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    • This publication is cited in the following 1 articles:
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    		Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
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    References:22
     
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