English

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

Complex Variables 2018-01-09 v1 Classical Analysis and ODEs

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.

Keywords

Cite

@article{arxiv.1801.02401,
  title  = {The Extremal Function for the Complex Ball for Generalized Notions of Degree and Multivariate Polynomial Approximation},
  author = {T. Bloom and L. Bos and N. Levenberg and S. Ma'u and F. Piazzon},
  journal= {arXiv preprint arXiv:1801.02401},
  year   = {2018}
}
R2 v1 2026-06-22T23:39:07.968Z