Journal d'Analyse Mathématique

, Volume 104, Issue 1, pp 69–82 | Cite as

Universal Taylor series have a strong form of universality

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Abstract

We prove that a function f holomorphic in a simply connected domain Ω whose Taylor series at ξ ∈ Ω is universal with respect to overconvergence automatically has a strong kind of universality: its expansion in Faber series corresponding to any connected compact set Γ ⊂ Ω with
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connected is universal, and we may take a supremum over all such Γ’s in a compact set. The topology used here is the Carathéodory topology. This answers a question of Mayenberger and Müller.

Keywords

Natural Number Compact Subset Holomorphic Function Taylor Series Uniform Convergence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© The Hebrew University of Jerusalem 2008

Authors and Affiliations

  1. 1.Laboratoire Bordelais d’Analyse et de Géométrie, UMR 5467Université Bordeaux 1Talence CedexFrance
  2. 2.Department of Mathematics, PanepistimiopilisUniversity of AthensAthensGreece

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