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Sbornik: Mathematics, 2002, Volume 193, Issue 6, Pages 811–823
DOI: https://doi.org/10.1070/SM2002v193n06ABEH000658
(Mi sm658)
 

This article is cited in 31 scientific papers (total in 31 papers)

On the Baker–Gammel–Wills conjecture in the theory of Padé approximants

V. I. Buslaev

Steklov Mathematical Institute, Russian Academy of Sciences
References:
Abstract: The well-known Padé conjecture, which was formulated in 1961 by Baker, Gammel, and Wills states that for each meromorphic function $f$ in the unit disc $D$ there exists a subsequence of its diagonal Padé approximants converging to $f$ uniformly on all compact subsets of $D$ not containing the poles of $f$. In 2001, Lubinsky found a meromorphic function in $D$ disproving Padé's conjecture.
The function presented in this article disproves the holomorphic version of Padé's conjecture and simultaneously disproves Stahl's conjecture (Padé's conjecture for algebraic functions).
Received: 24.12.2001
Bibliographic databases:
Document Type: Article
UDC: 517.524
MSC: 41A21, 30E10
Language: English
Original paper language: Russian
Citation: V. I. Buslaev, “On the Baker–Gammel–Wills conjecture in the theory of Padé approximants”, Sb. Math., 193:6 (2002), 811–823
Citation in format AMSBIB
\Bibitem{Bus02}
\by V.~I.~Buslaev
\paper On the Baker--Gammel--Wills conjecture in the~theory of Pad\'e approximants
\jour Sb. Math.
\yr 2002
\vol 193
\issue 6
\pages 811--823
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\crossref{https://doi.org/10.1070/SM2002v193n06ABEH000658}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1957951}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0036621513}
Linking options:
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  • https://doi.org/10.1070/SM2002v193n06ABEH000658
  • https://www.mathnet.ru/eng/sm/v193/i6/p25
  • This publication is cited in the following 31 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник - 1992–2005 Sbornik: Mathematics
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    Abstract page:616
    Russian version PDF:263
    English version PDF:12
    References:57
    First page:2
     
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