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
2019 Annales Polonici Mathematici  
We discuss the Siciak-Zakharyuta 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. 2010 Mathematics Subject Classification: Primary 32U15, 41A10.
doi:10.4064/ap180322-19-11 fatcat:4qdwsgshgfgvlkrvlazwvtn56m