Subclasses of Universal Taylor Series and center independence

2020/02/09 by Vagia Vlachou, Vlachou, Vagia · 1 citation
Mathematics · #30K05 #47A16 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2002.03304

openalex publication_date 2020/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A holomorphic function f on a simply connected domain Ω belongs to a subclass of universal Taylor series if prescribed and infinite number of partial sums of the Taylor expansion of f around a given center ζ₀ realize Mergalyan-type approximations outside Ω. We will prove that this class is independent of the choice of center if the indices of the partial sums do not grow very fast to infinity.

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