Direct and inverse results on row sequences of generalized Padé approximants to polynomial expansions
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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 Classification30E10 41A21 41A25 41A27
Key words and phrasesorthogonal polynomials Faber polynomials Padé approximation rate of convergence inverse result
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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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