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Determination of a universal series
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| File | Description | Size | Format | |
|---|---|---|---|---|
| Nikos_DeterminationUniversal.pdf | 236.75 kB | Adobe PDF | Download |
| 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 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theorem | Other versions: | http://www.heldermann.de/CMF/CMF12/CMF121/cmf12013.htm | Language: | en | Status of Item: | Not peer reviewed |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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