# Wydawnictwa / Czasopisma IMPAN / Annales Polonici Mathematici / Artykuły Online First

## The extremal function for the complex ball for generalized notions of degree and multivariate polynomial approximation

Annales Polonici Mathematici MSC: Primary 32U15, 41A10. DOI: 10.4064/ap180322-19-11 Opublikowany online: 28 March 2019

#### Streszczenie

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.

#### Autorzy

• T. BloomDepartment of Mathematics
University of Toronto
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• L. BosDepartment of Computer Science
University of Verona
Verona, Italy
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• N. LevenbergDepartment of Mathematics
Indiana University
Bloomington, IN, U.S.A.
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• S. Ma’uDepartment of Mathematics
University of Auckland Auckland, New Zealand
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• F. PiazzonDepartment of Mathematics