A generalization of universal Taylor series in simply connected domains

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Title: A generalization of universal Taylor series in simply connected domains
Authors: Tsirivas, Nikolaos
Permanent link: http://hdl.handle.net/10197/3893
Date: Apr-2012
Abstract: Let Ω be a simply connected proper subdomain of the complex plane and z0 be a point in Ω. It is known that there are holomorphic functions f on Ω for which the partial sums (Sn(f,z0)) of the Taylor series about z0 have universal approximation properties outside Ω. In this paper we investigate what can be said for the sequence (βnSn(f,z0)) when (βn) is a sequence of complex numbers. We also study a related analogue of a classical theorem of Seleznev concerning the case where the radius of convergence of the universal power series is zero.
Funding Details: Science Foundation Ireland
Type of material: Journal Article
Publisher: Elsevier
Journal: Journal of Mathematical Analysis and Applications
Volume: 388
Issue: 1
Start page: 261
End page: 369
Copyright (published version): 2011 Elsevier Inc
Keywords: Universal seriesCesàro hypercyclicityUniversalityHypercyclicityBernstein–Walsh TheoremSeleznev Theorem
Subject LCSH: Series, Taylor's
DOI: 10.1016/j.jmaa.2011.11.038
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

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