Examples of discrete operators with a pure point spectrum of finite multiplicity
type: Item
instance of: scholarly article
title: Examples of discrete operators with a pure point spectrum of finite multiplicity
zbMATH Open document ID: 0920.47026
author: Jean-Claude Guillot
author: Laurent Amour
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-04-27T00:00:00Z
review text: The following results are given in the present paper: Result 1. Given a certain diagonal matrix \(D\) and a perturbation \(P\) on \(\ell^2(\mathbb{Z}^m)\), then there exist a diagonal matrix \(\widehat D\) and an invertible matrix \(V\) such that \(V^{-1}(P+\widehat D)V= D\). Result 2. Given a certain diagonal matrix \(D\) and a discrete operator \(Q\) on \(\ell^2(\mathbb{Z}^m)^N\), where \(N\) is an \(n\)-integer, then there exist a diagonal matrix \(\widehat D\) and an invertible matrix \(V\) such that \(V^{-1}(Q+\widehat D)V= D\). The proofs of these results are based on some useful lemmas.
Mathematics Subject Classification ID: 47B37
Mathematics Subject Classification ID: 47A10
zbMATH DE Number: 1246310
zbMATH Keywords: diagonal matrix
zbMATH Keywords: perturbation
zbMATH Keywords: invertible matrix
reviewed by: K. Chandrasekhara Rao
MaRDI profile type: Publication
cites work: Pure point spectrum for discrete almost periodic Schrödinger operators
cites work: Examples of discrete Schrödinger operators with pure point spectrum
Recommended article: Examples of discrete Schrödinger operators with pure point spectrum
Recommended article: Examples of multidimensional, almost periodic operators, whose point and continuous spectra intersect
Recommended article: Q3733545
Recommended article: Discrete spectra of compactly perturbed bounded operators
Recommended article: Q3684547
Recommended article: On non-selfadjoint operators with finite discrete spectrum
Recommended article: A pointwise spectrum and representation of operators
Recommended article: Q5217134
Recommended article: On the point spectrum of discrete Schrödinger operator
Recommended article: Q5286513
description: scientific article; zbMATH DE number 1246310