Existence of universal Taylor series for non-simply connected domains

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Title: Existence of universal Taylor series for non-simply connected domains
Authors: Gardiner, Stephen J.
Permanent link: http://hdl.handle.net/10197/3842
Date: 27-May-2012
Abstract: It is known that, for any simply connected proper subdomain Ω of the complex plane and any point ζ in Ω, there are holomorphic functions on Ω that possess “universal” Taylor series expansions about ζ; that is, partial sums of the Taylor series approximate arbitrary polynomials on arbitrary compacta in ℂ\Ω that have connected complement. This paper shows, for nonsimply connected domains Ω, how issues of capacity, thinness and topology affect the existence of holomorphic functions on Ω that have universal Taylor series expansions about a given point.
Type of material: Journal Article
Publisher: Springer-Verlag
Copyright (published version): 2011 Springer Science+Business Media
Keywords: Taylor series;Universal approximation;Logarithmic capacity;Thin set;Overconvergence
Subject LCSH: Series
Approximation theory
Convergence
Potential theory (Mathematics)
Functions of complex variables
DOI: 10.1007/s00365-011-9133-z
Language: en
Status of Item: Not peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

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