Universal Taylor series, conformal mappings and boundary behaviour

Abstract

A holomorphic function f on a simply connected domain {\Omega} is said to possess a universal Taylor series about a point in {\Omega} if the partial sums of that series approximate arbitrary polynomials on arbitrary compacta K outside {\Omega} (provided only that K has connected complement). This paper shows that this property is not conformally invariant, and, in the case where {\Omega} is the unit disc, that such functions have extreme angular boundary behaviour.