On the essential spectrum of magnetic pseudodifferential operators

Măntoiu, Marius; Purice, Radu; Richard, Serge

doi:10.1016/j.crma.2006.11.001

Partial Differential Equations/Mathematical Physics

On the essential spectrum of magnetic pseudodifferential operators
[Sur le spectre essentiel des opérateurs pseudodifférentiels magnétiques]

Présenté par : Jean-Michel Bony

Măntoiu, Marius ¹ ; Purice, Radu ¹ ; Richard, Serge ²

¹ Institute of Mathematics Simion Stoilow of the Romanian Academy, P.O. Box 1-764, Bucharest, RO-014700, Romania
² Université de Lyon, Lyon, F-69003, France; Université Lyon 1, Institut Camille Jordan, Villeurbanne Cedex, F-69622, France; CNRS, UMR 5208, Villeurbanne Cedex, F-69622, France

Comptes Rendus. Mathématique, Tome 344 (2007) no. 1, pp. 11-14.

Résumé
Abstract

Nous étudions des opérateurs pseudodifférentiels magnétiques associés à des symboles elliptiques et ayant des potentiels anisotropes. Nous démontrons leur affiliation à certaines $C^{*}$ -algèbres et nous donnons des formules pour le spectre essentiel comme une union des spectres de certains opérateurs asymptotiques.

We study magnetic pseudodifferential operators associated with elliptic symbols and with anisotropic potentials. We prove affiliation to suitable $C^{*}$ -algebras and give formulae for the essential spectrum as a union of spectra of some asymptotic operators.

Reçu le : 2006-02-14
Accepté le : 2006-11-02
Publié le : 2006-12-11

DOI : 10.1016/j.crma.2006.11.001

Affiliations des auteurs :

Măntoiu, Marius ¹ ; Purice, Radu ¹ ; Richard, Serge ²

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Măntoiu, Marius; Purice, Radu; Richard, Serge. On the essential spectrum of magnetic pseudodifferential operators. Comptes Rendus. Mathématique, Tome 344 (2007) no. 1, pp. 11-14. doi : 10.1016/j.crma.2006.11.001. http://www.numdam.org/articles/10.1016/j.crma.2006.11.001/

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