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arXiv · 1801.02401

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

T. Bloom·L. Bos·N. Levenberg·S. Ma'u·F. Piazzon
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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.

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T. Bloom, L. Bos, N. Levenberg, S. Ma'u, F. Piazzon. 2018-01-08. The Extremal Function for the Complex Ball for Generalized Notions of Degree and Multivariate Polynomial Approximation. https://arxiv.org/abs/1801.02401

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