Computational Methods and Function Theory 6 (2006), No. 2, 437--446
Copyright Heldermann Verlag 2006
Christos Kariofillis
Department of Mathematics, Faculty of Sciences, Aristotel University of Thessaloniki, 54124 Thessaloniki, Greece.
Vassili Nestoridis
vnestor@math.uoa.gr , Department of Mathematics, University of Athens, 15784 Panepistimiopolis, Greece.
Let Ω be a simply connected domain in C. For a function f holomorphic in Ω let Sn(f,ζ) denote the partial sum of the Taylor development of f with center ζ∈Ω. We show that generically overconvergence phenomena of Sn(f,ζ) and their derivatives can occur on the boundary ∂Ω or in parts of it. In the rest of the boundary ∂Ω, the universal function f may be smooth. These parts of the boundary do not have to be connected.
Keywords: Generic property, overconvergence, Taylor series, natural boundary, universal functions.
MSC 2000: 30B30--41.
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