A refinement of the Helson-Szegö theorem and the determination of the extremal measures

Rodrigo Arocena

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The distribution of extremal points for Kergin interpolations : real case

Thomas Bloom, Jean-Paul Calvi (1998)

Annales de l'institut Fourier

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We show that a convex totally real compact set in $ℂ^{n}$ 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...