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arXiv · 1404.3409

Generic properties of Padé approximants and Padé universal series

Stéphane Charpentier·Vassili Nestoridis·Franck Wielonsky
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Abstract

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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Stéphane Charpentier, Vassili Nestoridis, Franck Wielonsky. 2014-04-13. Generic properties of Padé approximants and Padé universal series. https://arxiv.org/abs/1404.3409

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