Boundary behavior and Cesàro means of universal Taylor series.

@article{Bayart2006,
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.},
author = {Bayart, Frédéric},
journal = {Revista Matemática Complutense},
keywords = {Funciones de variable compleja; Desarrollo en serie de funciones; Series de Taylor; Sumabilidad Cesaro; universal series; Ostrowski gaps; overconvergence},
language = {eng},
number = {1},
pages = {235-247},
title = {Boundary behavior and Cesàro means of universal Taylor series.},
url = {http://eudml.org/doc/40887},
volume = {19},
year = {2006},
}

TY - JOUR
AU - Bayart, Frédéric
TI - Boundary behavior and Cesàro means of universal Taylor series.
JO - Revista Matemática Complutense
PY - 2006
VL - 19
IS - 1
SP - 235
EP - 247
AB - 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.
LA - eng
KW - Funciones de variable compleja; Desarrollo en serie de funciones; Series de Taylor; Sumabilidad Cesaro; universal series; Ostrowski gaps; overconvergence
UR - http://eudml.org/doc/40887
ER -