Subadjoint equations of index-1 linear singular difference equations
type: Item
instance of: scholarly article
title: Subadjoint equations of index-1 linear singular difference equations
zbMATH Open document ID: 1272.39002
author: Le Cong Loi
published in: Vietnam Journal of Mathematics
publication date: 2013-05-30T00:00:00Z
review text: The article deals with linear singular difference equations of the form \[ A_kx_{k+1} = B_kx_k, \quad k = 0,1,2,\ldots,N - 1,\tag{1} \] \(A_k, B_k \in {\mathbb R}^{m \times m}\), \(A_k\) are singular. Moreover, it is assumed that this equation is of index \(1\). Under these conditions it is proved that the subadjoint equation \[ A_{k-1}^Tu_k = B_k^Tu_{k+1}, \quad k = 0,1,2,\ldots,N - 1,\tag{2} \] is also of index \(1\). Also, the Lagrange identity discrete analogue and some relationships between equations (1) and (2) are obtained.
Mathematics Subject Classification ID: 39A06
zbMATH DE Number: 6168550
zbMATH Keywords: linear difference equation
zbMATH Keywords: adjoint equation
zbMATH Keywords: discrete Lagrange identity
zbMATH Keywords: index \(1\)
reviewed by: Peter P. Zabreĭko
MaRDI profile type: Publication
full work available at URL: s10013-013-0003-9
OpenAlex ID: W2083175559
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DOI: 10.1007/S10013-013-0003-9
description: scientific article; zbMATH DE number 6168550