THE DISTRIBUTION OF EXTREMAL POINTS FOR KERGIN INTERPOLATION - REAL CASE

We show that a convex totally real compact set in Cn admits an extrema l array for Kergin interpolation if and only if it is a totally real e llipse. (An array is said to be extremal for K when the corresponding sequence of Kergin interpolation polynomials converges uniformly ton K ) to the interpolated function as soon as it is holomorphic on a neigh borhood of K.). Extremal arrays on these ellipses are characterized in terms of the distribution of the points and the rate of convergence i s investigated. In passing, pie construct the first (higher dimensiona l) example of a compact convex set of non void interior that admits an extremal array without being circular.