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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2020, Volume 491, Pages 15–18
DOI: https://doi.org/10.31857/S268695432002006X (Mi danma44) 		 
This article is cited in 2 scientific papers (total in 2 papers)

MATHEMATICS

Constructive solution of one vector equilibrium problem

A. I. Bogolyubskii, V. G. Lysov

Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow, Russian Federation
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DOI: https://doi.org/10.31857/S268695432002006X
Abstract: We study a two-dimensional vector logarithmic-potential equilibrium problem with the Nikishin matrix of interaction. A constructive method for finding the supports of a vector equilibrium measure is given. The densities of the components of the equilibrium measure are expressed in terms of an algebraic function that is explicitly written out. The problem is motivated by the study of the convergence of the Frobenius–Padé and Hermite–Padé rational approximants.
Keywords: logarithmic potential, vector equilibrium problem, Nikishin matrix of interaction, equilibrium measure, Frobenius–Padé approximants, Hermite–Padé approximants.
Funding agency Grant number
Russian Science Foundation 19–71–30004
Lysov acknowledges the support of the Russian Science Foundation, project no. 19-71-30004.
Presented: B. N. Chetverushkin
Received: 26.12.2019
Revised: 26.12.2019
Accepted: 23.01.2020
English version:
Doklady Mathematics, 2020, Volume 101, Issue 2, Pages 90–92
DOI: https://doi.org/10.1134/S1064562420020064
Bibliographic databases:
Document Type: Article
UDC: 517.53
Language: Russian
Citation: A. I. Bogolyubskii, V. G. Lysov, “Constructive solution of one vector equilibrium problem”, Dokl. RAN. Math. Inf. Proc. Upr., 491 (2020), 15–18; Dokl. Math., 101:2 (2020), 90–92
Citation in format AMSBIB
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\by A.~I.~Bogolyubskii, V.~G.~Lysov
\paper Constructive solution of one vector equilibrium problem
\jour Dokl. RAN. Math. Inf. Proc. Upr.
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\pages 15--18
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\crossref{https://doi.org/10.31857/S268695432002006X}
\zmath{https://zbmath.org/?q=an:7424561}
\elib{https://elibrary.ru/item.asp?id=42860653}
\transl
\jour Dokl. Math.
\yr 2020
\vol 101
\issue 2
\pages 90--92
\crossref{https://doi.org/10.1134/S1064562420020064}
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    		Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
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