Abstract
We establish properties concerning the distribution of poles of Padé approximants, which are generic in Baire category sense. We also investigate Padé universal series, an analog of classical universal series, where Taylor partial sums are replaced with Padé 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 Padé universal series. We also show how Padé universal series can be built from classical universal series with large Ostrowski-gaps.
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Charpentier, S., Nestoridis, V. & Wielonsky, F. Generic properties of Padé approximants and Padé universal series. Math. Z. 281, 427–455 (2015). https://doi.org/10.1007/s00209-015-1493-9
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DOI: https://doi.org/10.1007/s00209-015-1493-9