The extremal function for the complex ball for generalized notions of degree and multivariate polynomial approximation
Volume 123 / 2019
Annales Polonici Mathematici 123 (2019), 171-195
MSC: Primary 32U15, 41A10.
DOI: 10.4064/ap180322-19-11
Published online: 28 March 2019
Abstract
We discuss the Siciak–Zakharyuta extremal function of pluripotential theory for the unit ball in ${\mathbb {C}}^d$ 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.
