Nonstationary Szegö theorem, band sequences and maximum entropy
type: Item
instance of: scholarly article
title: Nonstationary Szegö theorem, band sequences and maximum entropy
zbMATH Open document ID: 0652.47013
DOI: 10.1007/BF01236651
published in: Integral Equations and Operator Theory
publication date: 1988-01-01T00:00:00Z
review text: The authors obtain generalizations of well-known results relating to positive definite extensions of banded Toeplitz matrices. These extensions arise from the author's study, in this paper, of ``m- sequences'', which are those sequences of linearly independent vectors in Hilbert space whose orthonormalizing matrix \(A=(a_{ij})\), given via the Gram-Schmidt process, is m-banded, i.e., satisfies \(a_{ij}=0\) for \(| i-j| >m\). The authors apply their results to obtain a method for finding among vectors \(\{v_ j\}\) for which the inner product \(<v_ i,v_ j>=a_{ij}\) those for which the distance from \(v_ k\) to the linear span of \(v_ 0,...,v_{k-1}\) is maximal for every \(k\geq 0\).
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 47A20
zbMATH DE Number: 4063846
zbMATH Keywords: positive definite extensions of banded Toeplitz matrices
zbMATH Keywords: m-sequences
zbMATH Keywords: Gram-Schmidt process
author: Asher Ben-Artzi
author: I. Gohberg
reviewed by: Jeffrey R. Butz
MaRDI profile type: Publication
cites work: The maximum distance problem and band sequences
cites work: Invertible Selfadjoint Extensions of Band Matrices and Their Entropy
full work available at URL: https://doi.org/10.1007/bf01236651
OpenAlex ID: W2050056184
description: scientific article; zbMATH DE number 4063846