Essential spectrum of pseudodifferential operators with operator-valued symbols
type: Item
instance of: scholarly article
title: Essential spectrum of pseudodifferential operators with operator-valued symbols
zbMATH Open document ID: 1236.47047
DOI: 10.1134/S1064562411060317
published in: Doklady Mathematics
publication date: 2012-01-06T00:00:00Z
review text: The author considers the Fredholm property of the essential spectrum of pseudodifferential operators with operator-valued symbols for which the study of the Fredholm property is reduced to the analysis of their local invertibility at infinity by means of the method of limit operators of the author et al. This method has proved to be an effective tool for the study of the essential spectrum of operators in quantum mechanics, their discrete models, and the behavior of eigenfunctions of the discrete spectrum at infinity. An application to quantum wave guides is considered. Two types of electric potentials are analyzed in detail: (i) slowly oscillating at infinity and (ii) perturbation of periodic potentials by slowly oscillating ones.
reviewed by: Rémi Vaillancourt
Mathematics Subject Classification ID: 47G30
Mathematics Subject Classification ID: 47A53
Mathematics Subject Classification ID: 47N50
zbMATH DE Number: 5995567
zbMATH Keywords: essential spectrum
zbMATH Keywords: pseudodifferential operator
zbMATH Keywords: operator valued symbols
author: Vladimir Rabinovich
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5995567