Partially Smooth Universal Taylor Series on products of simply connected\n domains

2019/10/03 by Giorgos Kotsovolis, Kotsovolis, Giorgos
Mathematics · #30K05 #32A05 #32A17 #32A30 #Advanced Banach Space Theory #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1910.01759

openalex publication_date 2019/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using a recent Mergelyan type theorem, we show the existence of universal\nTaylor series on products of planar simply connected domains Oi that extend\ncontinuously on the product of the union of Oi with Si , where Si are subsets\nof the boundary of Oi, open in the relative topology. The universal\napproximation occurs on every product of compact sets Ki such that C - Ki are\nconnected and for some i0 it holds that Ki0 is contained in the complement of\nthe union of Oi0 with the closure of Si0. Furthermore,we introduce some\ntopological properties of universal Taylor series that lead to the voidance of\nsome families of functions.\n

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