Rapid Polynomial Approximation on Stein Manifolds

Audunn Skuta Snaebjarnarson

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arXiv · 1612.06173

Rapid Polynomial Approximation on Stein Manifolds

Audunn Skuta Snaebjarnarson

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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 $\mathbb{C}^N$ 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 $\mathbb{C}^N$ to its best uniform approximation by polynomials on a compact set.

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Audunn Skuta Snaebjarnarson. 2016-12-19. Rapid Polynomial Approximation on Stein Manifolds. https://arxiv.org/abs/1612.06173

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