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

2017/01/19 by Len Bos, Bos, Len, N. Levenberg +1 · 1 citation
Mathematics · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory

paper · doi:10.48550/arxiv.1701.05613

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.

Cited by

• Accelerating Multivariate Newton Interpolation in Downward Closed Polynomial Spaces

Related

• The Bernstein-Walsh-Siciak Theorem for analytic hypersurfaces
• Polynomials with exponents in compact convex sets and associated weighted extremal functions -- The Bernstein-Walsh-Siciak theorem
• Approximation of smooth functions using Bernstein polynomials in multiple variables
• Polynomial approximation on a compact subset of the real line
• Polynomials associated to non-convex bodies