On the asymptotic distribution of eigenvalues of banded matrices
type: Item
instance of: scholarly article
title: On the asymptotic distribution of eigenvalues of banded matrices
zbMATH Open document ID: 0646.15004
DOI: 10.1007/BF02075470
author: Walter Van Assche
author: Jeffrey S. Geronimo
author: Evans M. II Harrell
published in: Constructive Approximation
publication date: 1988-01-01T00:00:00Z
review text: This paper concerns the density of states for unbounded banded Hermitian matrices J with any band width and possibly variable off-diagonal elements, as they occur in some physical models. Two widely used definitions of a density-of-state measure (one based on taking functions of a truncate of J, and the other on truncating functions of J) are shown to be equivalent also in the unbounded case. Then the author discusses the variance of density of states under unbounded perturbations and the extension of those definitions to J's with unbounded essential spectrum, based on the known method of renormalizing the truncates of J so as to make them essentially bounded. Several examples are given.
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 47A70
Mathematics Subject Classification ID: 35P20
zbMATH DE Number: 4053808
zbMATH Keywords: asymptotic distribution of eigenvalues
zbMATH Keywords: unbounded banded Hermitian matrices
zbMATH Keywords: density-of-state measure
zbMATH Keywords: variance
zbMATH Keywords: unbounded perturbations
zbMATH Keywords: unbounded essential spectrum
reviewed by: Erwin O. Kreyszig
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02075470
OpenAlex ID: W2063208887
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description: scientific article; zbMATH DE number 4053808