Spectral theory of second-order vector difference equations
type: Item
instance of: scholarly article
title: Spectral theory of second-order vector difference equations
zbMATH Open document ID: 0934.39002
author: Yuming Shi
author: Shaozhu Chen
published in: Journal of Mathematical Analysis and Applications
publication date: 2000-04-26T00:00:00Z
review text: The paper deals with the boundary value problem \[ -\nabla (C_n\Delta x_n)+B_nx_n= \lambda\omega_n x_n,\quad n=1,2, \dots,N, \] \[ R{-x_0 \choose x_N}+ S{C_0\Delta x_0\choose C_N\Delta x_N}=0, \] where the matrices \(C_n\) may be singular. After a suitable definition of self-adjointness, corresponding spectral results, the dual orthogonality, Rayleigh's principles, minimax theorems and a comparison theorem for eigenvalues are obtained.
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 39A12
zbMATH DE Number: 1384918
zbMATH Keywords: vector difference equation
zbMATH Keywords: spectral theory
zbMATH Keywords: boundary value problem
zbMATH Keywords: spectral results
zbMATH Keywords: dual orthogonality
zbMATH Keywords: Rayleigh's principles
zbMATH Keywords: minimax theorems
zbMATH Keywords: eigenvalues
reviewed by: Lothar Berg
MaRDI profile type: Publication
full work available at URL: jmaa.1999.6510
OpenAlex ID: W2075172061
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DOI: 10.1006/JMAA.1999.6510
description: scientific article; zbMATH DE number 1384918