Interpolation by rational functions with nodes on the unit circle
type: Item
instance of: scholarly article
title: Interpolation by rational functions with nodes on the unit circle
zbMATH Open document ID: 0966.30031
DOI: 10.1023/A:1006433627981
author: Adhemar Bultheel
author: Erik Hendriksen
author: Olav Njåstad
author: Pablo González-Vera
published in: Acta Applicandae Mathematicae
publication date: 2001-08-06T00:00:00Z
review text: In this paper, the authors consider the convergence of the sequence of rational interpolations to a function \(f(z)\) which is analytic on the open unit disk and continuous in its closure. The interpolation functions have preassigned poles and the interpolation nodes are zeros of certain para-orthogonal functions with respect to a given absolutely continuous measure \(\mu\) on the unit circle. If \(\mu\) is the Lebesgue measure, the zeroes of the corresponding para-orthogonal polynomials are the roots of unity, which leads to the interpolation problem studied in \textit{J. L. Walsh} and \textit{A. Sharma} [Pac. J. Math. 14, 727-730 (1964; Zbl 0192.16802)].
reviewed by: Vladimir Bolotnikov
Mathematics Subject Classification ID: 30E05
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 65D30
zbMATH DE Number: 1546741
zbMATH Keywords: orthogonal rational functions
zbMATH Keywords: interpolation
MaRDI profile type: Publication
full work available at URL: a:1006433627981
OpenAlex ID: W1532098256
description: scientific article; zbMATH DE number 1546741