Full paper in PDF:
$%F. Bayart, Boundary Behavior and Cesàro Means of Universal Taylor Series, Rev. Mat. Complut. 19 (2006), no. 1, 235–247.%$

Boundary Behavior and Cesàro Means of Universal Taylor Series
Frédéric BAYART
Laboratoire Bordelais d’Analyse et de Géométrie
UMR 5467, Université Bordeaux 1
351 Cours de la Libération
F-33405 Talence cedex — France
 Frederic.Bayart@math.u-bordeaux1.fr

Received: July 26, 2005
Accepted: January 9, 2006
ABSTRACT

We study boundary properties of universal Taylor series. We prove that if f is a universal Taylor series on the open unit disk, then there exists a residual subset G of the unit circle such that f is unbounded on all radii with endpoints in G . We also study the effect of summability methods on universal Taylor series. In particular, we show that a Taylor series is universal if and only if its Cesàro means are universal.

Key words: cluster set, universality, overconvergence, Bernstein’s inequality.
2000 Mathematics Subject Classification: Primary 30B40. Secondary 30B10, 30D40, 30E10, 40G05.