Bernstein-Walsh theory associated to convex bodies and applications to multivariate approximation theory
Complex Variables
2017-01-23 v1 Classical Analysis and ODEs
Abstract
We prove a version of the Bernstein-Walsh theorem on uniform polynomial approximation of holomorphic functions on compact sets in several complex variables. Here we consider subclasses of the full polynomial space associated to a convex body P. As a consequence, we validate and clarify some observations of Trefethen in multivariate approximation theory.
Keywords
Cite
@article{arxiv.1701.05613,
title = {Bernstein-Walsh theory associated to convex bodies and applications to multivariate approximation theory},
author = {Len Bos and Norm Levenberg},
journal= {arXiv preprint arXiv:1701.05613},
year = {2017}
}