Discrete spectra criteria for certain classes of singular differential and difference operators
type: Item
instance of: scholarly article
title: Discrete spectra criteria for certain classes of singular differential and difference operators
zbMATH Open document ID: 1008.39011
DOI: 10.1016/S0898-1221(01)00170-5
publication date: 2002-06-13T00:00:00Z
review text: Criteria are established for discreteness and boundedness from below of the spectrum (the so-called property BD) for singular differential and difference operators of the form \[ m(y)\equiv {(-1)^n\over w(t)}\bigl(r(t) y^{(n)} \bigr)^{(n)}\quad \text{and} \quad b(y)_{k+n} \equiv{(-1)^n\over w_k} \Delta^n (r_k\Delta^n y_k), \] where \(n\in\mathbb{N}\), \(k\in\dot J=[n_0,\infty)\), \(n_0 \in \mathbb{N}\), the sequences \(r_k^{-1}\) and \(w_k\) are positive, real, and summable on \(\dot J\) while \(t\in \dot I=[a,+\infty)\), \(a\in\mathbb{R}\), and \(r^{-1}\), \(w\in L_{\text{loc}}(\dot I)\) are positive real functions.
reviewed by: Costică Moroşanu
Mathematics Subject Classification ID: 39A70
Mathematics Subject Classification ID: 34L05
Mathematics Subject Classification ID: 47E05
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 47B39
Mathematics Subject Classification ID: 34C10
zbMATH DE Number: 1755267
zbMATH Keywords: bounded spectra
zbMATH Keywords: discrete spectra
zbMATH Keywords: singular differential and difference operators
author: Roman Šimon Hilscher
MaRDI profile type: Publication
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full work available at URL: s0898-1221(01)00170-5
OpenAlex ID: W2066981465
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 1755267