The Nevanlinna-Pick problem on the closed unit disk: minimal norm rational solutions of low degree
type: Item
instance of: scholarly article
title: The Nevanlinna-Pick problem on the closed unit disk: minimal norm rational solutions of low degree
zbMATH Open document ID: 1262.30022
author: Vladimir Bolotnikov
author: Stephen P. Cameron
published in: Journal of Computational and Applied Mathematics
publication date: 2012-05-14T00:00:00Z
review text: A family of rational solutions of degree \(\leq n-1\) for the Nevanlinna-Pick interpolation problem with \(n\) interpolation conditions is constructed. Necessary and sufficient conditions for existence and uniqueness of solutions of this problem with minimal \(H^\infty\)-norm are established and a family of rational solutions of degree \(\leq n-1\) with a minimal norm is constructed in the indeterminate case. It is shown that if the interpolation nodes and the target values are unimodular, then any rational solution of degree \(\leq n-1\) is necessarily a Blaschke product. This expands a previous result by \textit{W. B. Jones} and \textit{S. Ruscheweyh} [Constructive Approximation 3, 405--409 (1987; Zbl 0634.41007)].
Mathematics Subject Classification ID: 30E05
zbMATH DE Number: 6035222
zbMATH Keywords: Pick matrix
zbMATH Keywords: minimal norm solution
zbMATH Keywords: low-degree rational solution
reviewed by: Thomas V. Tonev
MaRDI profile type: Publication
full work available at URL: j.cam.2012.02.009
OpenAlex ID: W2020901914
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DOI: 10.1016/J.CAM.2012.02.009
description: scientific article; zbMATH DE number 6035222