The distribution of extremal points for Kergin interpolations: real case
type: Item
instance of: scholarly article
title: The distribution of extremal points for Kergin interpolations: real case
zbMATH Open document ID: 0915.41001
author: Thomas Bloom
author: Jean-Paul Calvi
publication date: 1998-09-22T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/75276
review text: 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.
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A63
Mathematics Subject Classification ID: 32A05
zbMATH DE Number: 1202024
zbMATH Keywords: Kergin interpolation
zbMATH Keywords: polynomial approximation of holomorphic functions
zbMATH Keywords: logarithmic potentials
zbMATH Keywords: totally real sets
zbMATH Keywords: convergence criterion
zbMATH Keywords: rate of convergence
reviewed by: Eleonora A. Storozhenko
MaRDI profile type: Publication
OpenAlex ID: W2312900689
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DOI: 10.5802/AIF.1615
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 1202024