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.
@article{urn:eudml:doc:40887,
title = {Boundary behavior and Ces\`aro means of universal Taylor series.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {19},
year = {2006},
pages = {235-247},
zbl = {1103.30003},
mrnumber = {MR2219831},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:40887}
}
Bayart, Frédéric. Boundary behavior and Cesàro means of universal Taylor series.. Revista Matemática de la Universidad Complutense de Madrid, Tome 19 (2006) pp. 235-247. http://gdmltest.u-ga.fr/item/urn:eudml:doc:40887/