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 = \( \hat \sigma \) + r under additional constraints on the measure σ (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.
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Original Russian Text © A.A. Gonchar and S.P. Suetin, 2004, published in Sovremennye Problemy Matematiki, 2004, Vol. 5, pp. 3–66.
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Gonchar, A.A., Suetin, S.P. On Padé approximants of Markov-type meromorphic functions. Proc. Steklov Inst. Math. 272 (Suppl 2), 58–95 (2011). https://doi.org/10.1134/S0081543811030059
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DOI: https://doi.org/10.1134/S0081543811030059