Bernstein-Walsh theory associated to convex bodies and applications to multivariate approximation theory

Len Bos; Norm Levenberg

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arXiv · 1701.05613

Bernstein-Walsh theory associated to convex bodies and applications to multivariate approximation theory

Len Bos·Norm Levenberg

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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.

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Len Bos, Norm Levenberg. 2017-01-19. Bernstein-Walsh theory associated to convex bodies and applications to multivariate approximation theory. https://arxiv.org/abs/1701.05613

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