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Article Dans Une Revue Mathematische Zeitschrift Année : 2015

Generic properties of Padé approximants and Padé universal series

Résumé

We establish properties concerning the distribution of poles of Pad e approximants, which are generic in Baire category sense. We also investigate Pad e universal series, an analog of classical universal series, where Taylor partial sums are replaced with Pad e approximants. In particular, we complement previous studies on this subject by exhibiting dense or closed infi nite 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 Pad e universal series. We also show how Pad e universal series can be built from classical universal series with large Ostrowski-gaps.
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hal-00978170 , version 1 (13-04-2014)

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Stéphane Charpentier, Vassili Nestoridis, Franck Wielonsky. Generic properties of Padé approximants and Padé universal series. Mathematische Zeitschrift, 2015, 281 (1), ⟨10.1007/s00209-015-1493-9⟩. ⟨hal-00978170⟩
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