Universal Radial Approximation in Spaces of Analytic Functions

2021/06/07 by Konstantinos Maronikolakis, Maronikolakis, Konstantinos · 2 citations
Mathematics · #30E10 #30H10 #30K15 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2106.04002

openalex publication_date 2021/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Recently, Charpentier showed that there exist holomorphic functions f in the unit disk such that, for any proper compact subset K of the unit circle, any continuous function ϕ on K and any compact subset L of the unit disk, there exists an increasing sequence (r_n)_n∈ℕ⊆[0,1) converging to 1 such that |f(r_n(ζ-z)+z)-ϕ(ζ)|→0 as n→∞ uniformly for ζ∈ K and z∈ L. In this paper, we give analogues of this result for the Hardy spaces H^p(\mathbbD),1≤ p

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