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


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.


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

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