Universal Taylor series with respect to a prescribed subsequence

2020/06/23 by Augustin Mouze, Mouze, Augustin
Mathematics · #Analytic and geometric function 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.2006.12925

openalex publication_date 2020/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a holomorphic function f in the open unit disc \mathbbD and ζ∈\mathbbD, S_n(f,ζ) denotes the n-th partial sum of the Taylor development of f at ζ. Given an increasing sequence of positive integers μ=(μ_n), we consider the classes U(\mathbbD,ζ) (resp. U^(μ)(\mathbbD,ζ)) of such functions f such that the partial sums \S_n(f,ζ):n=1,2,…\ (resp. \S_μn(f,ζ):n=1,2,…\) approximate all polynomials uniformly on the compact sets K⊂\z∈ℂ:\vert z\vert≥ 1\ with connected complement. We show that these two classes of universal Taylor series coincide if and only if \limsup_n(\fracμ_n+1μ_n)

Citations

• Subclasses of Universal Taylor Series and center independence

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