Universal Taylor series in simply connected domains
type: Item
instance of: scholarly article
title: Universal Taylor series in simply connected domains
zbMATH Open document ID: 1122.30003
DOI: 10.1007/BF03321621
author: Christos Kariofillis
author: V. Nestoridis
published in: Computational Methods and Function Theory
publication date: 2007-05-14T00:00:00Z
review text: Let \(\Omega\) be a simply connected domain in the complex plane. The authors prove the existence of functions \(f\) holomorphic in \(\Omega\) which extend smoothly to some prescribed part \(S\) of the boundary \(\partial\Omega\) and having the property that, for every \(\zeta\in\Omega\), the sequence of partial sums \(S_n(f,\zeta)\) of the Taylor expansions with center \(\zeta\) exhibits universal overconvergence outside of \(\Omega\cup S\). This complements earlier results dealing with the special cases \(S = \emptyset\), that is universal overconvergence takes place outside of \(\Omega\), and \(S = \partial\Omega\), that is, \(f\) extends smoothly to \(\overline{\Omega}\).
Mathematics Subject Classification ID: 30B30
zbMATH DE Number: 5152625
zbMATH Keywords: overconvergence
zbMATH Keywords: universal Taylor series
zbMATH Keywords: universal functions
reviewed by: Jürgen Müller
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5152625