On the essential spectrum of magnetic pseudodifferential operators

Marius Măntoiu; Radu Purice; Serge Richard

doi:10.1016/j.crma.2006.11.001

Partial Differential Equations/Mathematical Physics

On the essential spectrum of magnetic pseudodifferential operators

Presented by: Jean-Michel Bony

Marius Măntoiu ¹; Radu Purice ¹; Serge Richard 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, Volume 344 (2007) no. 1, pp. 11-14.

Abstract
Résumé

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.

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.

Received: 2006-02-14
Accepted: 2006-11-02
Published online: 2006-12-11

DOI: 10.1016/j.crma.2006.11.001

Author's affiliations:

Marius Măntoiu ¹; Radu Purice ¹; Serge Richard 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

@article{CRMATH_2007__344_1_11_0,
     author = {Marius M\u{a}ntoiu and Radu Purice and Serge Richard},
     title = {On the essential spectrum of magnetic pseudodifferential operators},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {11--14},
     publisher = {Elsevier},
     volume = {344},
     number = {1},
     year = {2007},
     doi = {10.1016/j.crma.2006.11.001},
     language = {en},
}

TY  - JOUR
AU  - Marius Măntoiu
AU  - Radu Purice
AU  - Serge Richard
TI  - On the essential spectrum of magnetic pseudodifferential operators
JO  - Comptes Rendus. Mathématique
PY  - 2007
SP  - 11
EP  - 14
VL  - 344
IS  - 1
PB  - Elsevier
DO  - 10.1016/j.crma.2006.11.001
LA  - en
ID  - CRMATH_2007__344_1_11_0
ER  -

%0 Journal Article
%A Marius Măntoiu
%A Radu Purice
%A Serge Richard
%T On the essential spectrum of magnetic pseudodifferential operators
%J Comptes Rendus. Mathématique
%D 2007
%P 11-14
%V 344
%N 1
%I Elsevier
%R 10.1016/j.crma.2006.11.001
%G en
%F CRMATH_2007__344_1_11_0

Marius Măntoiu; Radu Purice; Serge Richard. On the essential spectrum of magnetic pseudodifferential operators. Comptes Rendus. Mathématique, Volume 344 (2007) no. 1, pp. 11-14. doi : 10.1016/j.crma.2006.11.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.11.001/

References
Cited by

[1] W.O. Amrein; A. Boutet de Monvel; V. Georgescu $C_{0}$ -Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians, Birkhäuser, Basel, 1996

[2] W.O. Amrein; M. Măntoiu; R. Purice Propagation properties for Schrödinger operators affiliated with certain $C^{*}$ -algebras, Ann. Inst. H. Poincaré, Volume 3 (2002), pp. 1215-1232

[3] V. Georgescu; A. Iftimovici Crossed products of $C^{*}$ -algebras and spectral analysis of quantum Hamiltonians, Comm. Math. Phys., Volume 228 (2002), pp. 519-560

[4] V. Georgescu; A. Iftimovici Localizations at infinity and essential spectrum of quantum Hamiltonians: I. General theory, Rev. Math. Phys., Volume 18 (2006), pp. 417-483

[5] B. Helffer; A. Mohamed Caractérisation du spectre essentiel de l'opérateur de Schrödinger avec un champ magnétique, Ann. Inst. Fourier, Volume 38 (1988), pp. 95-112

[6] M.V. Karasev; T.A. Osborn Symplectic areas, quantization and dynamics in electromagnetic fields, J. Math. Phys., Volume 43 (2002), pp. 756-788

[7] Y. Last; B. Simon The essential spectrum of Schrödinger, Jacobi, and CMV operators, J. Anal. Math., Volume 98 (2006), pp. 183-220

[8] M. Măntoiu; R. Purice The magnetic Weyl calculus, J. Math. Phys., Volume 45 (2004), pp. 1394-1417

[9] M. Măntoiu; R. Purice; S. Richard Twisted crossed products and magnetic pseudodifferential operators, Advances in Operator Algebras and Mathematical Physics, Theta Foundation, 2005, pp. 137-172

[10] M. Măntoiu, R. Purice, S. Richard, Spectral and propagation results for magnetic Schrödinger operators; a $C^{*}$ -algebraic framework, Preprint mp_arc 05-84

[11] V.S. Rabinovich Essential spectrum of perturbed pseudodifferential operators. Applications to the Schrödinger, Klein–Gordon, and Dirac operators, Russian J. Math. Phys., Volume 12 (2005), pp. 62-80

Cited by Sources:

Comments - Policy