The distribution of extremal points for Kergin interpolations : real case
We show that a convex totally real compact set in admits an extremal array for Kergin interpolation if and only if it is a totally real ellipse. (An array is said to be extremal for when the corresponding sequence of Kergin interpolation polynomials converges uniformly (on ) to the interpolated function as soon as it is holomorphic on a neighborhood of .). Extremal arrays on these ellipses are characterized in terms of the distribution of the points and the rate of convergence is investigated....