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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2022, Volume 62, Number 7, Pages 1115–1137
DOI: https://doi.org/10.31857/S0044466922050106 (Mi zvmmf11423) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Partial Differential Equations

Schwarz problem for $J$-analytic functions in an ellipse

V. G. Nikolaev

Yaroslav-the-Wise Novgorod State University, 173003, Novgorod the Great, Russia
Citations (1)
DOI: https://doi.org/10.31857/S0044466922050106
Abstract: The Schwarz problem for functions analytic in the sense of Douglis in an ellipse is considered. Necessary and sufficient conditions on the $l\times l$ matrix $J$ and the ellipse $\Gamma$ are obtained under which the Schwarz problem has a unique solution in Hölder classes. In the case of $l$ = 2 and matrices with distinct eigenvalues, the Schwarz problem is reduced to a scalar functional equation. Sufficient conditions on a Jordan basis of $J$ are obtained under which the Schwarz problem is solvable in an arbitrary ellipse. Matrices $J$ with eigenvalues lying above and below the real line are considered.
Key words: $J$-analytic functions, $\lambda$-holomorphic functions, eigenvalue of a matrix, ellipse, index of an operator.
Received: 14.11.2021
Revised: 14.11.2021
Accepted: 14.01.2022
English version:
Computational Mathematics and Mathematical Physics, 2022, Volume 62, Issue 7, Pages 1089–1111
DOI: https://doi.org/10.1134/S0965542522050104
Bibliographic databases:
Document Type: Article
UDC: 517.952
Language: Russian
Citation: V. G. Nikolaev, “Schwarz problem for $J$-analytic functions in an ellipse”, Zh. Vychisl. Mat. Mat. Fiz., 62:7 (2022), 1115–1137; Comput. Math. Math. Phys., 62:7 (2022), 1089–1111
Citation in format AMSBIB
\Bibitem{Nik22}
\by V.~G.~Nikolaev
\paper Schwarz problem for $J$-analytic functions in an ellipse
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2022
\vol 62
\issue 7
\pages 1115--1137
\mathnet{http://mi.mathnet.ru/zvmmf11423}
\crossref{https://doi.org/10.31857/S0044466922050106}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4466934}
\elib{https://elibrary.ru/item.asp?id=48621821}
\transl
\jour Comput. Math. Math. Phys.
\yr 2022
\vol 62
\issue 7
\pages 1089--1111
\crossref{https://doi.org/10.1134/S0965542522050104}
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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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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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