Generic properties of Pad\'e approximants and Pad\'e universal series
Functional Analysis
2014-04-15 v1 Classical Analysis and ODEs
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.
Cite
@article{arxiv.1404.3409,
title = {Generic properties of Pad\'e approximants and Pad\'e universal series},
author = {Stéphane Charpentier and Vassili Nestoridis and Franck Wielonsky},
journal= {arXiv preprint arXiv:1404.3409},
year = {2014}
}