We discuss the Siciak-Zakharyuta 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.
The Extremal Function for the Complex Ball for Generalized Notions of Degree and Multivariate Polynomial Approximation
L. Bos
;S. Mau;
2019-01-01
Abstract
We discuss the Siciak-Zakharyuta 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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