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Universal Taylor series for non-simply connected domains

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Alternative Title
Séries universelles de Taylor pour les domaines non-simplement connexes
Author(s)
Gardiner, Stephen J. 
Tsirivas, Nikolaos 
Uri
http://hdl.handle.net/10197/2465
Date Issued
May 2010
Date Available
28T14:19:19Z September 2010
Abstract
It is known that, for any simply connected proper subdomain Omega of the complex plane and any point zeta in Omega, there are holomorphic functions on Omega that have "universal" Taylor series expansions about zeta; that is, partial sums of the Taylor series approximate arbitrary polynomials on arbitrary compacta in C\Omega that have connected complement. This note shows that this phenomenon can break down for non-simply connected domains Omega, even when C\Omega is compact. This answers a question of Melas and disproves a conjecture of Müller, Vlachou and Yavrian.
Sponsorship
Science Foundation Ireland
Type of Material
Journal Article
Publisher
Elsevier
Journal
Comptes Rendus Mathématique
Volume
348
Issue
9-10
Start Page
521
End Page
524
Copyright (Published Version)
2010 Académie des sciences
Keywords
  • Taylor series

  • Universal functions

Subject – LCSH
Series, Taylor's
Analytic functions
DOI
10.1016/j.crma.2010.03.003
Web versions
http://dx.doi.org/10.1016/j.crma.2010.03.003
Language
English
Status of Item
Peer reviewed
ISSN
1631-073X
This item is made available under a Creative Commons License
https://creativecommons.org/licenses/by-nc-sa/1.0/
Owning collection
Mathematics and Statistics Research Collection
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