Uniform boundedness of Toeplitz matrices with variable coefficients
type: Item
instance of: scholarly article
title: Uniform boundedness of Toeplitz matrices with variable coefficients
zbMATH Open document ID: 1155.47029
author: A. Böttcher
author: S. M. Grudsky
published in: Integral Equations and Operator Theory
publication date: 2008-06-30T00:00:00Z
review text: Consider the \((N+1) \times (N+1)\) variable-coefficient Toeplitz matrix \(A_N(a)=(\hat{a}_{j-k}(j/N,k/N))^N_{j,k=0}\) generated by \(a(x,y,t)=\sum_{n=-\infty}^{\infty} \hat{a}_n(x,y)t^n\), where \(\hat{a}_n(x,y)= \int_{\mathbb{T}}a(x,y,t)t^{-n}\frac{| dt| }{2\pi}\). In this paper, the authors provide sufficient conditions on \(a\) that guarantee the uniform boundedness of the spectral norms \(\| A_N(a)\| _{\infty}\) as \(N \to \infty\).
reviewed by: Miyeon Kwon
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 65F35
zbMATH DE Number: 5294654
zbMATH Keywords: Toeplitz matrix
zbMATH Keywords: variable coefficients
zbMATH Keywords: matrix norm
zbMATH Keywords: Hölder continuity
MaRDI profile type: Publication
full work available at URL: s00020-008-1567-8
OpenAlex ID: W2082886440
DOI: 10.1007/S00020-008-1567-8
description: scientific article; zbMATH DE number 5294654