Partial Differential Equations/Mathematical Physics
On the essential spectrum of magnetic pseudodifferential operators
Comptes Rendus. Mathématique, Volume 344 (2007) no. 1, pp. 11-14.

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:
Accepted:
Published online:
DOI: 10.1016/j.crma.2006.11.001
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
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Măntoiu, Marius; Purice, Radu; Richard, Serge. 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. http://www.numdam.org/articles/10.1016/j.crma.2006.11.001/

[1] Amrein, W.O.; Boutet de Monvel, A.; Georgescu, V. C0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians, Birkhäuser, Basel, 1996

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

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

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

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

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

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

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

[9] Măntoiu, M.; Purice, R.; Richard, S. 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] Rabinovich, V.S. 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

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