Determination of a universal series

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Title: Determination of a universal series
Authors: Mouze, Augustin
Nestoridis, Vassili
Papadoperakis, Ioannis
Tsirivas, Nikolaos
Permanent link: http://hdl.handle.net/10197/4035
Date: Jan-2012
Abstract: The known proofs for universal Taylor series do not determine a specific universal Taylor series. In the present paper, we isolate a specific universal Taylor series by modifying the proof in [30]. Thus we determine all Taylor coefficients of a specific universal Taylor series on the disc or on a polygonal domain. Furthermore in non simply connected domains, when universal Taylor series exist, we can construct a sequence of specific rational functions converging to a universal function, provided the boundary is good enough. The solution uses an infinite denumerable procedure and a finite number of steps is not sufficient. However we solve a Runge's type problem in a finite number of steps.
Funding Details: Science Foundation Ireland
Type of material: Journal Article
Publisher: Heldermann Verlag
Journal: Computational Methods and Function Theory
Volume: 12
Issue: 1
Start page: 173
End page: 199
Copyright (published version): Heldermann Verlag 2012
Keywords: Universal seriesTaylor seriesRunge theorem
Other versions: http://www.heldermann.de/CMF/CMF12/CMF121/cmf12013.htm
Language: en
Status of Item: Not peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

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