The eigenvalue distribution of products of Toeplitz matrices - clustering and attraction
type: Item
instance of: scholarly article
title: The eigenvalue distribution of products of Toeplitz matrices - clustering and attraction
zbMATH Open document ID: 1202.15014
author: Debora Sesana
author: Elizabeth Strouse
author: Stefano Serra Capizzano
published in: Linear Algebra and its Applications
publication date: 2010-04-06T00:00:00Z
review text: Based on an earlier result of \textit{L. Golinskii} and \textit{S. Serra-Capizzano} [J. Approximation Theory, 144, No. 1, 84--102 (2007; Zbl 1111.15013)] establishing a link between distributions of non-Hermitian perturbations of Hermitian matrix sequences and the distribution of the original sequence, in this paper it is proved that the asymptotic spectrum of the product of Toeplitz sequences, whose symbols have a real-valued essentially bounded product \(h\), is described by the function \(h\) in the ''Szegö way''. Further, using Mergelyan's theorem, this result is extended to the more general case where \(h\) belongs to the Tilli class. An analogous result is obtained for sequences belonging to the algebra generated by Toeplitz sequences, if the symbols associated with the sequences are bounded and the global symbol \(h\) belongs to the Tilli class. Finaly, a generalization to the case of multilevel matrix-valued symbols is derived and the case of Laurent polynomials not necessarily belonging to the Tilli class is studied.
reviewed by: Mihail Voicu
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15B05
Mathematics Subject Classification ID: 15A12
Mathematics Subject Classification ID: 47B36
Mathematics Subject Classification ID: 47B65
zbMATH DE Number: 5689430
zbMATH Keywords: matrix sequence
zbMATH Keywords: joint eigenvalue distribution
zbMATH Keywords: Toeplitz matrix
MaRDI profile type: Publication
full work available at URL: j.laa.2009.12.005
OpenAlex ID: W2032690136
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DOI: 10.1016/J.LAA.2009.12.005
description: scientific article; zbMATH DE number 5689430