The Bernstein-Walsh-Siciak Theorem for analytic hypersurfaces

Abstract

As a first step towards a general set-theoretic counterpart of the remarkable Bernstein-Walsh-Siciak Theorem concerning the rapidity of polynomial approximation of a holomorphic function on polynomially convex compact sets in ${\mathbb{C}}^n$, we prove a version of this theorem for analytic hypersurfaces.

In this third version we slightly reorganized the paper, adding a new lemma explaining one of the estimates. This is the first part of a larger paper on the subject (in preparation)