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.
extremal function
complex ball
polynomial approximation
generalized notions of degree
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/1012043
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