%0 Journal Article
%T Generalized universal series
%+ Institut de Mathématiques de Marseille (I2M)
%+ Laboratoire Paul Painlevé - UMR 8524 (LPP)
%+ Centrale Lille
%A Charpentier, Stéphane
%A Mouze, Augustin
%A Munnier, Vincent
%< avec comité de lecture
%@ 0026-9255
%J Monatshefte für Mathematik
%I Springer Verlag
%V 179
%N 1
%8 2016-01
%D 2016
%Z 1401.1594
%R 10.1007/s00605-015-0764-1
%K Taylor series.
%K approximations by polynomials
%K Taylor series
%K universal series
%Z 30K05, 40A05, 41A10, 47A16
%Z Mathematics [math]/Functional Analysis [math.FA]Journal articles
%X We unify the recently developed abstract theories of universal series and extended universal series to include sums of the form \sum_k ak x_n,k for given sequences of vectors (x_n,k)n≥k≥0 in a topological vector space X. The algebraic and topological genericity as well as the spaceability are discussed. Then we provide various examples of such generalized universal series which do not proceed from the classical theory. In particular, we build universal series involving Bernstein's polynomials, we obtain a universal series version of MacLane's Theorem, and we extend a result of Tsirivas concerning universal Taylor series on simply connected domains, exploiting Bernstein- Walsh quantitative approximation theorem.
%G English
%2 https://hal.science/hal-00925108/document
%2 https://hal.science/hal-00925108/file/Generalized_CMM21.pdf
%L hal-00925108
%U https://hal.science/hal-00925108
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ I2M
%~ I2M-2014-
%~ UNIV-LILLE
%~ LPP-MATH