Full paper in PDF format:
$%E.S. Katsoprinakis,
Coincidence of Some Classes of Universal Functions, Rev. Mat. Complut. 22
(2009), no. 2, 427–445.%$
Coincidence of Some Classes of Universal
Functions
Emmanuel S. KATSOPRINAKIS
| University of Crete |
| Department of Mathematics |
| Knossou Ave. |
| GR-714 09 Heraklion, Crete — Greece |
| katsopr@math.uoc.gr |
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Received: February 25, 2008
Accepted: June 9, 2008
Let Ω be a domain in the complex plane such that Ω satisfies appropriate
geometrical and topological properties. We prove that if f is a holomorphic
function in Ω, then its Taylor series, with center at any ξ ∈ Ω, is universal with
respect to overconvergence if and only if its Cesàro (C,k)-means are universal
for any real k > -1. This is an extension of the same result, proved recently by
F. Bayart, for any integer k ≥ 0. As a consequence, several classes of universal
functions introduced in the related literature are shown to coincide.
Key words: Universal series, overconvergence, Taylor series, Cesàro means, Ostrowski
gaps.
2000 Mathematics Subject Classification: 30B30, 30B10, 30E10.