Rapid polynomial approximation on Stein manifolds
Volume 122 / 2019
Annales Polonici Mathematici 122 (2019), 81-100
MSC: Primary 32E30; Secondary 32A22, 32Q28, 32D15.
DOI: 10.4064/ap180711-13-11
Published online: 8 March 2019
Abstract
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 $\mathbb {C}^N$ and 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.
