Generic properties of Padé approximants and Padé universal series
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.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2014
- DOI:
- 10.48550/arXiv.1404.3409
- arXiv:
- arXiv:1404.3409
- Bibcode:
- 2014arXiv1404.3409C
- Keywords:
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- Mathematics - Functional Analysis;
- Mathematics - Classical Analysis and ODEs