Positive definite forms generated by integrals and weak limits
type: Item
instance of: scholarly article
title: Positive definite forms generated by integrals and weak limits
zbMATH Open document ID: 0541.46037
DOI: 10.1016/0022-247X(83)90274-3
author: Gideon Schechtman
author: Zvi Artstein
published in: Journal of Mathematical Analysis and Applications
publication date: 1983-01-01T00:00:00Z
review text: The authors prove the following interesting theorem: If \(M_ k\geq \epsilon I\) for \(\epsilon>0\), and if the sequence \(\| H_ k(t)\|^ 2\) is uniformly integrable over [0,1], then there exists a sequence \(D_ k(t)\) of measurable \(m\times m\) sign-changing matrix-valued functions such that a subsequence of \(H_ k(t)D_ k(t)\) converges weakly in \(L_ 2\) to, say, \(B_ 0(t)\) and \(\int^{1}_{0}B_ 0(t)B_ 0(t)'dt\) is positive definite.
Mathematics Subject Classification ID: 46G10
Mathematics Subject Classification ID: 47A56
Mathematics Subject Classification ID: 47B38
zbMATH DE Number: 3859768
zbMATH Keywords: positive definite forms
zbMATH Keywords: sign-changing matrix-valued functions
MaRDI profile type: Publication
cites work: Q5667036
description: scientific article; zbMATH DE number 3859768