The Extremal Function for the Complex Ball for Generalized Notions of Degree and Multivariate Polynomial Approximation

2018/01/08 by Bloom, T., Bos, L., Levenberg, N. +2
#32U15 #41A10 #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1801.02401

Abstract

We discuss the Siciak-Zaharjuta extremal function of pluripotential theory for the unit ball in C^d for spaces of polynomials with the notion of degree determined by a convex body P. We then use it to analyze the approximation properties of such polynomial spaces, and how these may differ depending on the function f to be approximated.

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