Coincidence of some classes of universal functions

Abstract

Let Ω a domain in the complex plane such that Ω satisfies appropriate geometrical and topological properties. We prove that if f is a holomorphic function in Ω, then its Taylor series, with center at any ξ Є Ω , is universal with respect to overconvergence if and only if its Cesáro (C, k)-means are universal for any real k > −1. This is an extension of the same result, proved recently by F. Bayart, for any integer k ≥ 0. As a consequence, several classes of universal functions introduced in the related literature are shown to coincide.