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Determination of a universal series

Author(s)
Mouze, Augustin  
Nestoridis, Vassili  
Papadoperakis, Ioannis  
Tsirivas, Nikolaos  
Uri
http://hdl.handle.net/10197/4035
Date Issued
2012-01
Date Available
2013-01-14T17:12:15Z
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.
Sponsorship
Science Foundation Ireland
Other Sponsorship
SFI RFP 09/RFP/MTH2149
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
Subjects

Universal series

Taylor series

Runge theorem

Web versions
http://www.heldermann.de/CMF/CMF12/CMF121/cmf12013.htm
Language
English
Status of Item
Not peer reviewed
This item is made available under a Creative Commons License
https://creativecommons.org/licenses/by-nc-nd/3.0/ie/
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Nikos_DeterminationUniversal.pdf

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Mathematics and Statistics Research Collection

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