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Russian Mathematical Surveys, 2011, Volume 66, Issue 6, Pages 1015–1048
DOI: https://doi.org/10.1070/RM2011v066n06ABEH004769 (Mi rm9452) 		 
This article is cited in 21 scientific papers (total in 21 papers)

Padé–Chebyshev approximants of multivalued analytic functions, variation of equilibrium energy, and the $S$-property of stationary compact sets

A. A. Gonchara, E. A. Rakhmanovba, S. P. Suetina

a Steklov Mathematical Institute, Russian Academy of Sciences
b University of South Florida
English version PDF (801 kB) Citations (21)
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DOI: https://doi.org/10.1070/RM2011v066n06ABEH004769
Abstract: Padé–Chebyshev approximants are considered for multivalued analytic functions that are real-valued on the unit interval $[-1,1]$. The focus is mainly on non-linear Padé–Chebyshev approximants. For such rational approximations an analogue is found of Stahl's theorem on convergence in capacity of the Padé approximants in the maximal domain of holomorphy of the given function. The rate of convergence is characterized in terms of the stationary compact set for the mixed equilibrium problem of Green-logarithmic potentials.
Bibliography: 79 titles.
Keywords: rational approximation, Padé approximants, Chebyshev polynomials, non-linear Padé–Chebyshev approximants, stationary compact set, Stahl's theorem, convergence in capacity.
Received: 08.11.2011
Russian version:
Uspekhi Matematicheskikh Nauk, 2011, Volume 66, Issue 6(402), Pages 3–36
DOI: https://doi.org/10.4213/rm9452
Bibliographic databases:
Document Type: Article
UDC: 517.53
MSC: Primary 30E10, 31A15, 41A21; Secondary 30F99, 40A15
Language: English
Original paper language: Russian
Citation: A. A. Gonchar, E. A. Rakhmanov, S. P. Suetin, “Padé–Chebyshev approximants of multivalued analytic functions, variation of equilibrium energy, and the $S$-property of stationary compact sets”, Uspekhi Mat. Nauk, 66:6(402) (2011), 3–36; Russian Math. Surveys, 66:6 (2011), 1015–1048
Citation in format AMSBIB
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    • This publication is cited in the following 21 articles:
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