Rapid Polynomial Approximation on Stein Manifolds

2016/12/19 by Auðunn Skúta Snæbjarnarson, Snaebjarnarson, Audunn Skuta
Mathematics · #32A22 #32D15 #32E30 #32Q28 #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1612.06173

openalex publication_date 2016/12/19 · openalex created_date 2017/01/06 · openalex updated_date 2026/07/28

Abstract

In this paper we generalize to a certain class of Stein manifolds the Bernstein-Walsh-Siciak theorem which describes the equivalence between possible holomorphic continuation of a function f defined on a compact set K in ℂ^N to the rapidity of the best uniform approximation of f on K by polynomials. We also generalize Winiarski's theorem which relates the growth rate of an entire function f on ℂ^N to its best uniform approximation by polynomials on a compact set.

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