Overconvergent series of rational functions and universal Laurent series
type: Item
instance of: scholarly article
title: Overconvergent series of rational functions and universal Laurent series
zbMATH Open document ID: 1156.30030
author: B. E. Eshmatov
published in: Journal d'Analyse Mathématique
publication date: 2008-09-03T00:00:00Z
review text: Let \(f\) be some analytic function on a closed connected subset \(\Gamma\) of \(\mathbb{C}\) and \(\{ P_n\}\) a polynomial sequence converging to \(f\) on \(\Gamma\) with geometric rate, then, it was proved previously by first and last authors, the convergence of \(\{ P_n\}\) extends to certain maximal domain. The present paper generalizes this result to sequences of rational functions with fixed poles. It is shown that this result implies that two classes of universal Laurent-type series coincide.
reviewed by: Jacek Gilewicz
Mathematics Subject Classification ID: 30E10
Mathematics Subject Classification ID: 30B30
zbMATH DE Number: 5320476
MaRDI profile type: Publication
full work available at URL: s11854-008-0023-7
OpenAlex ID: W2003058370
cites work: UNIVERSAL LAURENT SERIES
cites work: UNIVERSAL APPROXIMATION PROPERTIES OF OVERCONVERGENT POWER SERIES ON OPEN SETS
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cites work: UNIVERSAL OVERCONVERGENCE AND OSTROWSKI-GAPS
cites work: Q4328333
cites work: On some classes of universal functions
cites work: Coincidence of Two Classes of Universal Laurent Series
DOI: 10.1007/S11854-008-0023-7
description: scientific article; zbMATH DE number 5320476