The distribution of extremal points for Kergin interpolations: real case
We show that a convex totally real compact set in \(\mathbb C^n\) 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 \(K\) when the corresponding sequence of Kergin interpolation polynomials converges uniformly (on \(K\)) to the interpolated function as soon as it is holomorphic on a neighborhood of \(K\)). Extremal arrays on these ellipses are characterized in terms of the distribution of the points and the rate of convergence is investigated. In passing, we construct the first (higher dimensional) example of a compact convex set of non void interior that admits an extremal array without being circular.
polynomial approximation of holomorphic functions
scientific article; zbMATH DE number 1202024
scientific article