Uniform Approximation of Extremal Functions in Weighted Bergman Spaces

2017/05/18 by Timothy Ferguson, Ferguson, Timothy
Mathematics · #30H20 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1705.06710

openalex publication_date 2017/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss approximation of extremal functions by polynomials in the weighted Bergman spaces A^p_α where -1 < α< 0 and -1 < α< p-2. We obtain bounds on how close the approximation is to the true extremal function in the A^p_α and uniform norms. We also discuss several results on the relation between the Bergman modulus of continuity of a function and how quickly its best polynomial approximants converge to it.

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