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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
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
Citation:
V. I. Buslaev, “On the Baker–Gammel–Wills conjecture in the theory of Padé approximants”, Sb. Math., 193:6 (2002), 811–823
Linking options:
https://www.mathnet.ru/eng/sm658https://doi.org/10.1070/SM2002v193n06ABEH000658 https://www.mathnet.ru/eng/sm/v193/i6/p25
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Abstract page: | 616 | Russian version PDF: | 263 | English version PDF: | 12 | References: | 57 | First page: | 2 |
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