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Acta Mathematica Hungarica

, Volume 157, Issue 1, pp 191–219 | Cite as

Direct and inverse results on row sequences of generalized Padé approximants to polynomial expansions

  • N. BosuwanEmail author
Article
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Abstract

Starting from the orthogonal and Faber polynomial expansions of a function F, we study the asymptotic behaviors of two generalized Padé approximations (orthogonal Padé approximation and Padé–Faber approximation). We obtain both direct and inverse results relating the convergence of the poles of these approximants and the singularities of F. Thereby, we obtain analogues of theorems by A. A. Gonchar and S. P. Suetin.

Mathematics Subject Classification

30E10 41A21 41A25 41A27 

Key words and phrases

orthogonal polynomials Faber polynomials Padé approximation rate of convergence inverse result 

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Notes

Acknowledgement

I wish to express my gratitude toward the anonymous referee for careful reading, helpful comments, and suggestions leading to improvements of this work. I also want to thank Prof. Guillermo López Lagomasino for insight on the topic of this paper.

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceMahidol UniversityRatchathewi District, BangkokThailand
  2. 2.Centre of Excellence in Mathematics, CHEBangkokThailand

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