Some limit relations for multidimensional positive-definite Toeplitz matrices
type: Item
instance of: scholarly article
title: Some limit relations for multidimensional positive-definite Toeplitz matrices
zbMATH Open document ID: 0658.47031
DOI: 10.1007/BF01077721
author: V. B. Adamyan
publication date: 1988-01-01T00:00:00Z
review text: Let \(G_ 1\subset G_ 2\subset..\). be an increasing sequence of bounded regions in \({\mathbb{R}}^ p_+=\{\bar x=(x_ 1,...,x_ n):\) \(\forall n\) \(x_ n>0\}\) and \(G_ 1\cup...\cup G_ n\cup...={\mathbb{R}}^ p_+\), \(G'_ n=G\cap {\mathbb{Z}}^ p\). Let \(I_ n=\| g^{(n)}_{k,\ell}\|\) \(((k,\ell)\in G'_ n)\) be a positive Toeplitz matrix. \(I_ n^{-1}=\| \tilde g^{(n)}_{k,\ell}\|\) and \(d_ n=\sum_{(k,\ell)\in G'_ n}\tilde g^{(n)}_{k,\ell}.\) The aim of this paper is to study of asymptotic behaviour of \(d_ n\) when \(n\to \infty\).
Mathematics Subject Classification ID: 47B35
zbMATH DE Number: 4075893
zbMATH Keywords: Toeplitz matrix
zbMATH Keywords: asymptotic behaviour
reviewed by: V. M. Deundjak
MaRDI profile type: Publication
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 4075893