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 \({\varOmega }_i\), \(i=1,\ldots ,d\). The universal approximation is realized by partial sums of the Taylor development of the universal function on products of planar compact sets \(K_i\), \(i=1,\ldots ,d\) such that \({\mathbb {C}}-K_i\) is connected and for at least one \(i_0\) the set \(K_{i_0}\) is disjoint from \({\varOmega }_{i_0}\).