Universal Taylor series, conformal mappings and boundary behaviour

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Title: Universal Taylor series, conformal mappings and boundary behaviour
Authors: Gardiner, Stephen J.
Permanent link: http://hdl.handle.net/10197/5645
Date: Dec-2013
Online since: 2014-06-18T14:08:50Z
Abstract: A holomorphic function f on a simply connected domain Ω is said to possess a universal Taylor series about a point in Ω if the partial sums of that series approximate arbitrary polynomials on arbitrary compacta K outside Ω (provided only that K has connected complement). This paper shows that this property is not conformally invariant, and, in the case where Ω is the unit disc, that such functions have extreme angular boundary behaviour.
Funding Details: Science Foundation Ireland
Type of material: Journal Article
Publisher: Annales De L'Institit Fourier
Journal: Annales De L'Institit Fourier(Grenoble)
Volume: 63
Issue: 6
Start page: 327
End page: 339
Copyright (published version): 2013 the authors
Keywords: Complex variables
Other versions: http://arxiv.org/abs/1301.2082
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

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