Spectral theory of Sturm-Liouville difference operators
type: Item
instance of: scholarly article
title: Spectral theory of Sturm-Liouville difference operators
zbMATH Open document ID: 1158.39013
author: Guoliang Shi
author: Hongyou Wu
published in: Linear Algebra and its Applications
publication date: 2008-12-12T00:00:00Z
review text: This paper deals with eigenvalue problems for the discrete Sturm-Liouville problem \[ -\Delta(f\Delta y)(n)+q(n)y(n)=\lambda w(n)y(n) \] for \(n=1,\dots,k\). The authors present several classes of explicit self-adjoint Sturm-Liouville difference operator with either a non-Hermitian leading coefficient function, or a non-Hermitian potential function, or a non-definite weight function, or a non-self-adjoint boundary condition. It is shown that a discrete Sturm-Liouville problem admits a difference operator realization if and only if it does not have all complex numbers as eigenvalues. Spectral properties of self-adjoint Sturm-Liouville difference operators are studied.
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 39A70
Mathematics Subject Classification ID: 47B39
Mathematics Subject Classification ID: 34L05
zbMATH DE Number: 5382424
zbMATH Keywords: discrete Sturm-Liouville problem
zbMATH Keywords: self-adjointness
zbMATH Keywords: spectral theory
zbMATH Keywords: comparison of eigenvalues
zbMATH Keywords: eigenvalue problems
zbMATH Keywords: Sturm-Liouville difference operator
reviewed by: Weinian Zhang
MaRDI profile type: Publication
full work available at URL: j.laa.2008.09.035
OpenAlex ID: W2160755502
cites work: Discrete and continuous boundary problems
cites work: Sturmian and spectral theory for discrete symplectic systems
cites work: Q4797834
cites work: Trace formulas and Borg-type theorems for matrix-valued Jacobi and Dirac finite difference operators
cites work: Second-order Sturm-Liouville difference equations and orthogonal polynomials
cites work: Spectral theory of second-order vector difference equations
cites work: Q3836536
DOI: 10.1016/J.LAA.2008.09.035
description: scientific article; zbMATH DE number 5382424