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Izv. RAN. Ser. Mat., 2021, Volume 85, Issue 3, Pages 13–29 (Mi izv9047)  

On a lower bound for the rate of convergence of multipoint Padé approximants of piecewise analytic functions

V. I. Buslaev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: We obtain a lower bound for the rate of convergence of multipoint Padé approximants of functions holomorphically extendable from a compact set to a union of domains whose boundaries possess a symmetry property. The bound obtained matches a known upper bound for the same quantity.

Keywords: rational approximation, orthogonal polynomials, Padé approximants, distribution of poles, convergence in capacity.

Funding Agency Grant Number
Russian Science Foundation 19-11-00316
This paper was written with the support of the Russian Science Foundation (grant no. 19-11-00316).


DOI: https://doi.org/10.4213/im9047

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English version:
Izvestiya: Mathematics, 2021, 85:3, 351–366

Bibliographic databases:

UDC: 517.53
MSC: 30E10, 41A21, 41A25, 41A28
Received: 31.03.2020
Revised: 01.04.2020

Citation: V. I. Buslaev, “On a lower bound for the rate of convergence of multipoint Padé approximants of piecewise analytic functions”, Izv. RAN. Ser. Mat., 85:3 (2021), 13–29; Izv. Math., 85:3 (2021), 351–366

Citation in format AMSBIB
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