Boundedness, regularity and smoothness of universal Taylor series

摘要

Let Ω be an unbounded simply connected domain in $mathbb{C}$ satisfying some topological assumptions; for example let Ω be an open half-plane. We show that there exists a bounded holomorphic function on Ω which extends continuously on $bar{Omega}$ and is a universal Taylor series in Ω in the sense of Luh and Chui–Parnes with respect to any center. Our proof uses Arakeljan’s Approximation Theorem.