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.
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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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Dedicated to Professor Guillermo López Lagomasino on the occasion of his 70th birthday
The research of N. Bosuwan was supported by the Strengthen Research Grant for New Lecturer from the Thailand Research Fund and the Office of the Higher Education Commission (MRG6080133) and Faculty of Science, Mahidol University.
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Bosuwan, N. Direct and inverse results on row sequences of generalized Padé approximants to polynomial expansions. Acta Math. Hungar. 157, 191–219 (2019). https://doi.org/10.1007/s10474-018-0878-8
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DOI: https://doi.org/10.1007/s10474-018-0878-8