Mathematische Zeitschrift

, Volume 284, Issue 3–4, pp 919–946 | Cite as

Polynomial inequalities and universal Taylor series

  • Augustin MouzeEmail author
  • Vincent Munnier


We derive several new properties concerning both universal Taylor series and Fekete universal series from classical polynomial inequalities. In particular, we study some density properties of their approximating subsequences. Moreover we exhibit summability methods which preserve or imply the universality of Taylor series in the complex plane. Likewise we show that the partial sums of the Taylor expansion around zero of a \(C^{\infty }\) function is universal if and only if the sequence of its Cesàro means satisfies the same universal approximation property.


Universal series Frequently universal series Bernstein inequality Density 

Mathematics Subject Classification

30K05 47A16 32A40 40A05 41A10 



We are indebted to the anonymous referee for useful comments and suggestions which considerably improved the presentation of the paper.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Laboratoire Paul PainlevéUMR 8524, Cité ScientifiqueVilleneuve d’Ascq CedexFrance
  2. 2.École Centrale de LilleCité ScientifiqueVilleneuve d’Ascq CedexFrance

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