Remarks on the Boundedness of Poles of Padé-orthogonal and Padé-Faber approximants
Issued Date
2023-09-30
Resource Type
ISSN
16860209
Scopus ID
2-s2.0-85184265117
Journal Title
Thai Journal of Mathematics
Volume
2023
Issue
Special Issue
Start Page
147
End Page
159
Rights Holder(s)
SCOPUS
Bibliographic Citation
Thai Journal of Mathematics Vol.2023 No.Special Issue (2023) , 147-159
Suggested Citation
Supuang A., Bosuwan N. Remarks on the Boundedness of Poles of Padé-orthogonal and Padé-Faber approximants. Thai Journal of Mathematics Vol.2023 No.Special Issue (2023) , 147-159. 159. Retrieved from: https://repository.li.mahidol.ac.th/handle/20.500.14594/97191
Title
Remarks on the Boundedness of Poles of Padé-orthogonal and Padé-Faber approximants
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Author's Affiliation
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Abstract
Given a function F holomorphic on a neighborhood of some compact subset of the complex plane, we prove that if the zeros of the denominators of (n, mn) orthogonal Padé and Padé-Faber approximants remain uniformly bounded on a sequence of indices {(n, mn)} satisfying sup{mn: n Ԑ N} < ∞. then either F is a polynomial or F has a singularity in the complex plane. In this paper, we relax a condition on the indices mn in results from [N. Bosuwan, On the boundedness of poles of generalized Padé approximants, Adv. Differ. Equ 2019 (137) (2019) https://doi.org/10.1186/sl36fi2-01fl-2081-fl].