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Sbornik: Mathematics, 2015, Volume 206, Issue 2, Pages 175–200
DOI: https://doi.org/10.1070/SM2015v206n02ABEH004453 (Mi sm8428) 		 
This article is cited in 20 scientific papers (total in 20 papers)

Convergence of $m$-point Padé approximants of a tuple of multivalued analytic functions

V. I. Buslaevab

a Steklov Mathematical Institute of Russian Academy of Sciences
b Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow
English version PDF (593 kB) Citations (20)
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DOI: https://doi.org/10.1070/SM2015v206n02ABEH004453
Abstract: We prove the convergence of $m$-point Padé approximants of an $m$-tuple of holomorphic germs that admit analytic continuation along all paths in the extended complex plane that do not pass through a finite set of points. This result extends Stahl's theorem from the case $m=1$ to the case of an arbitrary $m\in\mathbb N$.
Bibliography: 15 titles.
Keywords: rational approximation, orthogonal polynomials, Padé approximants, convergence in capacity, limiting distribution of poles.
Funding agency Grant number
Russian Science Foundation 14-21-00025
This research was supported by the Russian Science Foundation under grant no. 14-21-00025.
Received: 28.07.2014
Russian version:
Matematicheskii Sbornik, 2015, Volume 206, Number 2, Pages 5–30
DOI: https://doi.org/10.4213/sm8428
Bibliographic databases:
Document Type: Article
UDC: 517.53
MSC: 41A21, 30E10, 42C05
Language: English
Original paper language: Russian
Citation: V. I. Buslaev, “Convergence of $m$-point Padé approximants of a tuple of multivalued analytic functions”, Mat. Sb., 206:2 (2015), 5–30; Sb. Math., 206:2 (2015), 175–200
Citation in format AMSBIB
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    • This publication is cited in the following 20 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:630
    Russian version PDF:177
    English version PDF:6
    References:50
    First page:33
     
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