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Universal Taylor series on products of planar domains. (English) Zbl 1469.30118

Summary: 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 \({\varOmega}_{i_0}\).

MSC:

30K05 Universal Taylor series in one complex variable
32A05 Power series, series of functions of several complex variables
32A17 Special families of functions of several complex variables
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