On the essential spectrum of magnetic pseudodifferential operators
type: Item
instance of: scholarly article
title: On the essential spectrum of magnetic pseudodifferential operators
zbMATH Open document ID: 1113.47036
author: Marius Măntoiu
author: Radu Purice
author: Serge Richard
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2007-02-14T00:00:00Z
review text: In [\textit{M.\,Mantoiu} and \textit{R.\,Purice}, J.~Math.\ Phys.\ 45, No.\,4, 1394--1417 (2004; Zbl 1068.81043)], the first two authors defined a gauge-covariant quantization for a particle in a magnetic field, extending the Weyl pseudodifferential calculus. In the present paper, the authors interpret the resulting pseudodifferential operators (associated with elliptic symbols and anisotropic potentials) as observables affiliated to an appropriate \(C^*\)-algebra. Using this approach, they obtain a decomposition of the essential spectrum of such an operator into a union of essential spectra of special operators prescribed by the asymptotic behavior of the magnetic field and potential. This leads to an extension of some localization results of \textit{W.\,O.\,Amrein, M.\,Mantoiu} and \textit{R.\,Purice} [Ann.\ Henri Poincaré 3, No.\,6, 1215--1232 (2002; Zbl 1029.81066)].
Mathematics Subject Classification ID: 47G30
Mathematics Subject Classification ID: 35S05
Mathematics Subject Classification ID: 47C15
Mathematics Subject Classification ID: 81Q10
Mathematics Subject Classification ID: 81R15
zbMATH DE Number: 5126416
zbMATH Keywords: magnetic PsDO
zbMATH Keywords: magnetic Moyal product
zbMATH Keywords: magnetic Moyal *-algebra
zbMATH Keywords: twisted crossed product
reviewed by: Anatoly N. Kochubei
MaRDI profile type: Publication
full work available at URL: j.crma.2006.11.001
OpenAlex ID: W2113908373
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DOI: 10.1016/J.CRMA.2006.11.001
description: scientific article; zbMATH DE number 5126416