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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2020, Volume 311, Pages 213–227
DOI: https://doi.org/10.4213/tm4146 (Mi tm4146) 		 
This article is cited in 13 scientific papers (total in 13 papers)

Mixed Type Hermite–Padé Approximants for a Nikishin System

V. G. Lysov

Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047 Russia
Full-text PDF (245 kB) Citations (13)
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DOI: https://doi.org/10.4213/tm4146
Abstract: We consider the problem of mixed type Hermite–Padé approximants and prove that the Nikishin system is perfect for this problem. Using the method of a vector equilibrium problem, we find weak asymptotics and prove the convergence of the approximants along any rays in the index table. We also present an equivalent statement in the form of a matrix Riemann–Hilbert problem.
Keywords: mixed type Hermite–Padé approximants, Nikishin system, perfect system, vector logarithmic-potential equilibrium problem, convergence of rational approximants, matrix Riemann–Hilbert problem.
Received: April 22, 2020
Revised: June 23, 2020
Accepted: July 21, 2020
English version:
Proceedings of the Steklov Institute of Mathematics, 2020, Volume 311, Pages 199–213
DOI: https://doi.org/10.1134/S0081543820060127
Bibliographic databases:
Document Type: Article
UDC: 517.53
Language: Russian
Citation: V. G. Lysov, “Mixed Type Hermite–Padé Approximants for a Nikishin System”, Analysis and mathematical physics, Collected papers. On the occasion of the 70th birthday of Professor Armen Glebovich Sergeev, Trudy Mat. Inst. Steklova, 311, Steklov Math. Inst., Moscow, 2020, 213–227; Proc. Steklov Inst. Math., 311 (2020), 199–213
Citation in format AMSBIB
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\paper Mixed Type Hermite--Pad\'e Approximants for a Nikishin System
\inbook Analysis and mathematical physics
\bookinfo Collected papers. On the occasion of the 70th birthday of Professor Armen Glebovich Sergeev
\serial Trudy Mat. Inst. Steklova
\yr 2020
\vol 311
\pages 213--227
\publ Steklov Math. Inst.
\publaddr Moscow
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    • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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