Generic power series on subsets of the unit disk

@article{Maga2022,
abstract = {We examine the boundary behaviour of the generic power series $f$ with coefficients chosen from a fixed bounded set $\Lambda $ in the sense of Baire category. Notably, we prove that for any open subset $U$ of the unit disk $D$ with a nonreal boundary point on the unit circle, $f(U)$ is a dense set of $\mathbb \{C\}$. As it is demonstrated, this conclusion does not necessarily hold for arbitrary open sets accumulating to the unit circle. To complement these results, a characterization of coefficient sets having this property is given.},
author = {Maga, Balázs, Maga, Péter},
journal = {Czechoslovak Mathematical Journal},
keywords = {complex power series; boundary behaviour; Baire category},
language = {eng},
number = {3},
pages = {637-652},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Generic power series on subsets of the unit disk},
url = {http://eudml.org/doc/298425},
volume = {72},
year = {2022},
}

TY - JOUR
AU - Maga, Balázs
AU - Maga, Péter
TI - Generic power series on subsets of the unit disk
JO - Czechoslovak Mathematical Journal
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 72
IS - 3
SP - 637
EP - 652
AB - We examine the boundary behaviour of the generic power series $f$ with coefficients chosen from a fixed bounded set $\Lambda $ in the sense of Baire category. Notably, we prove that for any open subset $U$ of the unit disk $D$ with a nonreal boundary point on the unit circle, $f(U)$ is a dense set of $\mathbb {C}$. As it is demonstrated, this conclusion does not necessarily hold for arbitrary open sets accumulating to the unit circle. To complement these results, a characterization of coefficient sets having this property is given.
LA - eng
KW - complex power series; boundary behaviour; Baire category
UR - http://eudml.org/doc/298425
ER -