On a moment problem for rational matrix-valued functions.
type: Item
instance of: scholarly article
title: On a moment problem for rational matrix-valued functions.
zbMATH Open document ID: 1046.47016
DOI: 10.1016/S0024-3795(03)00579-2
author: Andreas Lasarow
author: B. Fritzsche
author: B. Kirstein
published in: Linear Algebra and its Applications
publication date: 2003-10-15T00:00:00Z
review text: Given a block matrix \(G\) and a sequence of complex numbers which are not located on the unit circle \(\mathbb T\), the authors consider the moment problem for rational matrix-valued functions, which entails describing the set \(\mathcal M\) of all nonnegative Hermitian Borel measures \(F\) on \(\mathbb T\) having \(G\) as the Gramian matrix. This problem can be considered as a generalization of two problems: the truncated trigonometric moment problem for matrix polynomials and the classical Carathéodory-Nevanlinna-Pick interpolation problem. The main result of the paper determines when the set \({\mathcal M}\) is nonempty and when the measure \(F\) belongs to \({\mathcal M}\) or not. In the case in which the moment problem for rational matrix-valued functions has a solution and the given matrix is nonsingular, the authors explicitly construct a particular solution.
Mathematics Subject Classification ID: 47A57
Mathematics Subject Classification ID: 44A60
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 1993116
zbMATH Keywords: nonnegative Hermitian Borel measures on the unit circle
zbMATH Keywords: finite rational matrix moment problem
reviewed by: Zenon Jan Jabłoński
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1993116