ON BEST APPROXIMATION OF THE MONOMIALS ON THE UNIT BALL OF R-R

Bos and Liang have separately proved that the Kergin interpolants with respect to distinguished nodes on the unit disk are best approximatio ns of the monomials in the infinity norm. These results are extended b y characterizing the nodes as solutions of a system of nonlinear equat ions. Thus, it is possible to get all nodes with this property on the unit disk and it is likewise possible to lift results to the ball in t he sense of approximation in the mean. (C) 1998 Academic Press.