Universal Taylor series for non-simply connected domains

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Title: Universal Taylor series for non-simply connected domains
Authors: Gardiner, Stephen J.
Tsirivas, Nikolaos
Permanent link: http://hdl.handle.net/10197/2465
Date: May-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.
Funding Details: 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 seriesUniversal functions
Subject LCSH: Series, Taylor's
Analytic functions
DOI: 10.1016/j.crma.2010.03.003
Other versions: http://dx.doi.org/10.1016/j.crma.2010.03.003
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

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