The partial trigonometric moment problem on an interval: The matrix case
type: Item
instance of: scholarly article
title: The partial trigonometric moment problem on an interval: The matrix case
zbMATH Open document ID: 0833.42004
DOI: 10.1016/0024-3795(93)00330-3
author: Daniel Alpay
author: Philippe Loubaton
published in: Linear Algebra and its Applications
publication date: 1995-10-09T00:00:00Z
review text: Let \(\varphi_1, \varphi_2,\dots, \varphi_N\) be a sequence of \(p\times p\) matrices, and let \([- \omega,\omega]\subseteq [-\pi, \pi]\). The following partial trigonometric moment problem on an interval is considered: Characterize the set \(\mu(\omega)\) of all \(p\times p\) matrix- valued positive measures carried by \([-\omega, \omega]\) for which \(\varphi_k= \int^\pi_{-\pi} e^{-ikt} d\mu(t)\) for \(k= 0, 1,\dots, N\). In the scalar case \((p= 1)\) Akhiezer and Krein have proved this problem. Using a new approach, the authors solve the matrix version of the partial trigonometric moment problem on an interval in the nondegenerate case.
Mathematics Subject Classification ID: 42A70
zbMATH DE Number: 803716
zbMATH Keywords: matrix moment problem on the interval
zbMATH Keywords: partial trigonometric moment problem
reviewed by: B. P. Osilenker
MaRDI profile type: Publication
full work available at URL: 0024-3795(93)00330-3
OpenAlex ID: W2015561329
cites work: Q4284398
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Wikidata QID: Q127720396
description: scientific article; zbMATH DE number 803716