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 Ω i , 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 K i , i = 1, . . . , d such that C − K i is connected and for at least one i 0 the set K i0 is disjoint from Ω i0 .

No abstract

No 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.

No abstract