Universal Taylor Series Without Baire and the Influence of J.-P. Kahane

In this paper I present my first proof regarding the existence of universal Taylor series on the disc where the universal approximation was required on the boundary as well. It is a modification of a construction giving a negative answer to a question of S. Pichorides, where the approximation was valid only on the boundary of the disc. There was no use of Baire’s theorem in the above proofs. J.-P. Kahane suggested to use Baire’s theorem which yields stronger results with simpler proofs. Later, Baire’s theorem was systematically used in order to establish new generic universalities.