Doubly universal Taylor Series on simply connected domains

TL;DR

This paper investigates the existence of doubly universal Taylor series on simply connected domains, extending previous results from the unit disk to more general domains, highlighting new universality properties in complex analysis.

Contribution

It generalizes the concept of doubly universal Taylor series from the unit disk to any simply connected domain, broadening the scope of universality in complex approximation theory.

Findings

Established the existence of doubly universal Taylor series on simply connected domains.

Extended previous results from the unit disk to more general domains.

Provided new conditions for universality in complex Taylor series.

Abstract

In this article we deal with the existence of doubly universal Taylor series defined on simply connected domains with respect to any center and we generalize the results of G. Costakis and N. Tsirivas for the unit disk.