The Extremal Function for the Complex Ball for Generalized Notions of Degree and Multivariate Polynomial Approximation
- Resource Type
- Working Paper
- Authors
- Bloom, T.; Bos, L.; Levenberg, N.; Ma'u, S.; Piazzon, F.
- Source
- Subject
- Mathematics - Complex Variables
Mathematics - Classical Analysis and ODEs
32U15, 41A10
- Language
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.