%0 Journal Article
%T Generic properties of Padé approximants and Padé universal series
%+ Institut de Mathématiques de Marseille (I2M)
%+ Department of Mathematics [Athens]
%A Charpentier, Stéphane
%A Nestoridis, Vassili
%A Wielonsky, Franck
%< avec comité de lecture
%@ 0025-5874
%J Mathematische Zeitschrift
%I Springer
%V 281
%N 1
%8 2015
%D 2015
%Z 1404.3409
%R 10.1007/s00209-015-1493-9
%K universal Taylor series
%K Padé approximant
%K generic property
%Z 41A21, 30K05, 41A10
%Z Mathematics [math]/Functional Analysis [math.FA]
%Z Mathematics [math]/Classical Analysis and ODEs [math.CA]Journal articles
%X 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.
%G English
%2 https://hal.science/hal-00978170/document
%2 https://hal.science/hal-00978170/file/Pade-gen9Avr14-sans-label.pdf
%L hal-00978170
%U https://hal.science/hal-00978170
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ INSMI
%~ I2M
%~ I2M-2014-