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JOURNALS // Sovremennye Problemy Matematiki // Archive

Sovrem. Probl. Mat., 2004 Issue 5, Pages 3–67 (Mi spm8)

This article is cited in 12 papers

On Padé Approximants of Meromorphic Functions of Markov Type

A. A. Gonchar, S. P. Suetin


Abstract: The paper is devoted to the asymptotic properties of diagonal Padé approximants for Markov-type meromorphic functions. The main result is strong asymptotic formulas for the denominators of diagonal Padé approximants for Markov-type meromorphic functions $f=\widehat\sigma+r$ under additional constraints on the measure $\sigma$ ($r$ is a rational function). On the basis of these formulas, it is proved that, in a sufficiently small neighborhood of a pole of multiplicity $m$ of such a meromorphic function $f$, all poles of the diagonal Padé approximants $f_n$ are simple and asymptotically located at the vertices of a regular $m$-gon.

UDC: 517.53

DOI: 10.4213/spm8


 English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2011, 272, suppl. 2, S58–S95

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