Partially Smooth Universal Taylor Series on products of simply connected domains

Abstract

Using a recent Mergelyan type theorem, we show the existence of universal Taylor series on products of planar simply connected domains Ω i that extend continuously onopen in the relative topology. The universal approximation occurs on every product of compact sets K i such that C − K i are connected and for some i 0 it holds K i0 ∩ (Ω i0 ∪ S i0 ) = ∅. Furthermore, we introduce some topological properties of universal Taylor series that lead to the voidance of some families of functions.