Displaying similar documents to “Extremal points in the space C n ”

Disks extremal with respect to interpolation constants.

Nguyen Van Trao (2000)

Publicacions Matemàtiques

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We define a function μ from the set of sequences in the unit ball to R* by taking the greatest lower bound of the reciprocal of the interpolating constant of the sequences of the disk which get mapped to the given sequence by a holomorphic mapping from the disk to the ball. Its properties are studied in the spirit of the work of Amar and Thomas.

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...