Boundary behaviour of functions which possess universal Taylor series

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Title: Boundary behaviour of functions which possess universal Taylor series
Authors: Gardiner, Stephen J.
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Date: Feb-2013
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 establishes a strong unboundedness property for such functions near every boundary point. The result is new even in the case of the disc, where it strengthens work of several authors.
Type of material: Journal Article
Publisher: Oxford Journals
Journal: Bulletin of the London Mathematical Society
Volume: 45
Issue: 1
Start page: 191
End page: 199
Copyright (published version): 2013, Oxford Journals
Keywords: Taylor seriesHolomorphic functions
DOI: 10.1112/blms/bds078
Language: en
Status of Item: Not peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

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