On the point spectrum of discrete Schrödinger operator
type: Item
instance of: scholarly article
title: On the point spectrum of discrete Schrödinger operator
zbMATH Open document ID: 0813.47040
DOI: 10.1007/BF01075284
author: Serguei Naboko
author: S. I. Yakovlev
publication date: 1994-04-12T00:00:00Z
review text: Consider the discrete Schrödinger operator \(L\) defined by \[ Lu_ n= u_{n+ 1}+ u_{n- 1}+ q_ n u_ n,\qquad n= 1,2,\dots\;. \] The equation for eigenvalues \(\lambda\) of \(L\), \(Lu= \lambda u\), means that a certain sequence \(u_ \lambda= \{u_ n\}^ \infty_{n= 1}\in \ell_ 2\) satisfies the relation \[ Lu_ n= \lambda u_ n,\qquad n= 1,2,\dots \] with \(u_ 0= 0\). In the present paper the authors have obtained two results giving a precise condition for an eigenvalue of \(L\) to appear in the interval \((-2,2)\), depending on the following two parameters: the decay law of the potential \(q\) and the distance from \(\lambda\) to the boundary of the continuous spectrum.
reviewed by: B. G. Pachpatte
Mathematics Subject Classification ID: 47B39
zbMATH DE Number: 525656
zbMATH Keywords: discrete Schrödinger operator
zbMATH Keywords: equation for eigenvalues
zbMATH Keywords: boundary of the continuous spectrum
MaRDI profile type: Publication
cites work: Q4185363
cites work: Zur Spektraltheorie von Sturm-Liouville-Operatoren
cites work: Some Jacobi matrices with decaying potential and dense point spectrum
cites work: Examples of discrete Schrödinger operators with pure point spectrum
cites work: Spectral behavior of quasi periodic potentials
full work available at URL: https://doi.org/10.1007/bf01075284
OpenAlex ID: W2988949696
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 525656