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Sbornik: Mathematics, 2016, Volume 207, Issue 9, Pages 1236–1266
DOI: https://doi.org/10.1070/SM8448 (Mi sm8448) 		 
This article is cited in 12 scientific papers (total in 12 papers)

The Gonchar-Stahl $\rho^2$-theorem and associated directions in the theory of rational approximations of analytic functions

E. A. Rakhmanovab

a University of South Florida, Tampa, FL, USA
b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
English version PDF (707 kB) Citations (12) Russian version article
References:
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DOI: https://doi.org/10.1070/SM8448
Abstract: The Gonchar-Stahl $\rho^2$-theorem characterizes the rate of convergence of best uniform (Chebyshev) rational approximations (with free poles) for one basic class of analytic functions. The theorem itself, modifications and generalizations of it, methods involved in its proof and other related details constitute an important subfield in the theory of rational approximations of analytic functions and complex analysis.
This paper briefly outlines the essentials of the subfield. The fundamental contributions of A. A. Gonchar and H. Stahl are at the heart of the exposition.
Bibliography: 70 titles.
Keywords: rational approximations, Padé approximants, orthogonal polynomials, equilibrium distributions, stationary compact set, $S$-property.
Received: 26.10.2014 and 10.04.2016
Bibliographic databases:
Document Type: Article
UDC: 517.53
MSC: Primary 30E10, 41A20, 41A25; Secondary 41A21
Language: English
Original paper language: Russian
Citation: E. A. Rakhmanov, “The Gonchar-Stahl $\rho^2$-theorem and associated directions in the theory of rational approximations of analytic functions”, Sb. Math., 207:9 (2016), 1236–1266
Citation in format AMSBIB
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\vol 207
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\pages 1236--1266
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    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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