Universal Laurent series in finitely connected domains
type: Item
instance of: scholarly article
title: Universal Laurent series in finitely connected domains
zbMATH Open document ID: 1154.30004
author: B. E. Eshmatov
published in: Archiv der Mathematik
publication date: 2008-09-12T00:00:00Z
review text: For a simply connected domain in the complex plane \(\mathbb{C}\), \textit{A. D. Melas} and \textit{V. Nestoridis} [Adv. Math. 157, No. 2, 138--176 (2001; Zbl 0985.30023)] discussed the existence of universal Taylor series. Then \textit{G. Costakis, V. Nestoridis}, and \textit{I. Papadoperakis} [Proc. Edinb. Math. Soc. (2) 48, No. 3, 571--583 (2005; Zbl 1151.30301)] replaced Taylor series by Laurent series and considered the existence of universal Laurent series. Let \(\Omega\) be a finitely connected domain in \(\mathbb{C}\), and assume that \((\mathbb{C}\cup {\infty})\setminus \Omega\) has finitely many components, the paper under review proves that it is possible to demand universal approximation to a part of the boundary \(\partial \Omega\) while on the remaining part the universal function can be smooth.
Mathematics Subject Classification ID: 30B30
zbMATH DE Number: 5343873
zbMATH Keywords: overconvergence
zbMATH Keywords: universal function
zbMATH Keywords: generic property
reviewed by: Zongsheng Gao
MaRDI profile type: Publication
full work available at URL: s00013-008-2470-x
OpenAlex ID: W1994849606
DOI: 10.1007/S00013-008-2470-X
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description: scientific article; zbMATH DE number 5343873