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Displaying similar documents to “On an extremal function and domains of convergence of series of homogeneous polynomials”

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 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...

Homogeneous extremal function for a ball in ℝ²

Mirosław Baran (1999)

Annales Polonici Mathematici

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We point out relations between Siciak’s homogeneous extremal function Ψ B and the Cauchy-Poisson transform in case B is a ball in ℝ². In particular, we find effective formulas for Ψ B for an important class of balls. These formulas imply that, in general, Ψ B is not a norm in ℂ².