Determination of a universal series
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|Title:||Determination of a universal series||Authors:||Mouze, Augustin
|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 . 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 series; Taylor series; Runge theorem||Other versions:||http://www.heldermann.de/CMF/CMF12/CMF121/cmf12013.htm||Language:||en||Status of Item:||Not peer reviewed|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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