Generic properties of Pad, approximants and Pad, universal series

摘要

We establish properties concerning the distribution of poles of Pad, approximants, which are generic in Baire category sense. We also investigate Pad, universal series, an analog of classical universal series, where Taylor partial sums are replaced with Pad, 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 Pad, universal series. We also show how Pad, universal series can be built from classical universal series with large Ostrowski-gaps.