The \({\mathcal L}^ p\) space of a positive definite matrix of measures and density of matrix polynomials in \({\mathcal L}^ 1\)
type: Item
instance of: scholarly article
title: The \({\mathcal L}^ p\) space of a positive definite matrix of measures and density of matrix polynomials in \({\mathcal L}^ 1\)
zbMATH Open document ID: 0886.46029
author: A. J. Durán
author: Pedro Lopez-Rodriguez
published in: Journal of Approximation Theory
publication date: 1997-09-04T00:00:00Z
review text: The authors consider the space \(L^p(\mu)\), where \(1\leq p\leq\infty\) and \(\mu\) is a positive definite matrix of measures. The paper contains six theorems and ten lemmas. The main results are theorems which say that \(L^p_n(\mu)\) is a Banach (Hilbert) space for some \(p\) and that the set of all positive definite matrices of measures having the same moments as those of \(\mu\) is compact in the vague topology. Moreover, the authors give a density result for \(L^1(\mu)\) which is an extension to the matrix case of the well-known result.
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 46E27
zbMATH DE Number: 1057418
zbMATH Keywords: positive definite matrices of measures
zbMATH Keywords: moments
zbMATH Keywords: compact in the vague topology
zbMATH Keywords: density
reviewed by: Aleksander Waszak
MaRDI profile type: Publication
full work available at URL: jath.1996.3073
OpenAlex ID: W2064592613
cites work: Density questions in the classical theory of moments
cites work: A generalization of Favard's theorem for polynomials satisfying a recurrence relation
cites work: On Orthogonal Polynomials With Respect to a Positive Definite Matrix of Measures
cites work: Markov's Theorem for Orthogonal Matrix Polynomials
cites work: Matrix inner product having a matrix symmetric second-order differential operator
cites work: Orthogonal matrix polynomials: zeros and Blumenthal's theorem
cites work: Density Questions for the Truncated Matrix Moment Problem
cites work: Orthogonal matrix polynomials and higher-order recurrence relations
cites work: Q3810043
cites work: Scattering theory and matrix orthogonal polynomials on the real line
cites work: Q4034496
cites work: Some approximation problems in $L^{p}$-spaces of matrix-valued functions
cites work: Inclusion Relations for SomeLp-Spaces of Operator-Valued Functions
cites work: Q5790034
cites work: The square-integrability of matrix-valued functions with respect to a non-negative Hermitian measure
cites work: Polynomial interpolation and Gaussian quadrature for matrix-valued functions
DOI: 10.1006/JATH.1996.3073
description: scientific article; zbMATH DE number 1057418