Spectral properties of Jacobi matrices by asymptotic analysis.
type: Item
instance of: scholarly article
title: Spectral properties of Jacobi matrices by asymptotic analysis.
zbMATH Open document ID: 1051.47026
DOI: 10.1016/S0021-9045(02)00038-2
author: Jan Janas
author: Marcin Moszyński
published in: Journal of Approximation Theory
publication date: 2003-04-02T00:00:00Z
review text: A key element of this paper is the formulation and an inversion-related proof of several discrete version(s) of the Levinson theorem and of the related spectral analysis (by the authors' own statement, the discretization approach to differential equations is a topic of independent interest). This is what leads to the main application, viz., to a successful determination of asymptotics of generalized (i.e., difference-equation-interpreted) eigensolutions of certain specific (two classes of) Jacobi matrices (with vanishing main diagonal and periodically perturbed power-law elements).
reviewed by: Miloslav Znojil
Mathematics Subject Classification ID: 47B36
Mathematics Subject Classification ID: 47B37
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 39A12
zbMATH DE Number: 1891290
zbMATH Keywords: Jacobi matrix
zbMATH Keywords: difference equation
zbMATH Keywords: asymptotic solution
zbMATH Keywords: generalized eigenvectors
zbMATH Keywords: spectral analysis
zbMATH Keywords: discrete Levinson theorem
zbMATH Keywords: power-law weights
zbMATH Keywords: periodic perturbation
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1891290