Universal Taylor Series on products of planar domains

Abstract

Using a recent Mergelyan type theorem for products of planar compact sets we establish generic existence of Universal Taylor Series on products of planar simply connected domains Omegai, i=1, . . . , d. The universal approximation is realized by partial sums of the Taylor development of the universal function on products of planar compact sets Ki, i=1, . . . , d such that the complement of Ki is connected and for at least one i0 the set Ki0 is disjoint from Omegai0.