Generic properties of Padé approximants and Padé universal series

We establish properties concerning the distribution of poles of Padé approximants, which are generic in Baire category sense. We also investigate Padé universal series, an analog of classical universal series, where Taylor partial sums are replaced with Padé approximants. In particular, we complemen...

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Bibliographic Details
Published in:Mathematische Zeitschrift 2015, Vol.281 (1-2), p.427-455
Main Authors: Charpentier, S., Nestoridis, V., Wielonsky, F.
Format: Article
Language:English
Subjects:
Classical Analysis and ODEs
Functional Analysis
Mathematics
Mathematics and Statistics
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Summary:We establish properties concerning the distribution of poles of Padé approximants, which are generic in Baire category sense. We also investigate Padé universal series, an analog of classical universal series, where Taylor partial sums are replaced with Padé approximants. In particular, we complement previous studies on this subject by exhibiting dense or closed infinite dimensional linear subspaces of analytic functions in a simply connected domain of the complex plane, containing the origin, whose all non zero elements are made of Padé universal series. We also show how Padé universal series can be built from classical universal series with large Ostrowski-gaps.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-015-1493-9