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Kioulafa, K.; Kotsovolis, G.; Nestoridis, V.
Complex analysis and its synergies, 06/2021, Volume: 7, Issue: 2Journal Article
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 i 0 is disjoint from Ω i 0 .
