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Proceedings of the American Mathematical Society

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The modulation mapping for magnetic symbols and operators


Authors: Marius Mantoiu and Radu Purice
Journal: Proc. Amer. Math. Soc. 138 (2010), 2839-2852
MSC (2010): Primary 35S05, 47L15; Secondary 47L65, 47L90
Published electronically: April 2, 2010
MathSciNet review: 2644897
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Abstract: We extend the Bargmann transform to the magnetic pseudodifferential calculus, using gauge-covariant families of coherent states. We also introduce modulation mappings, a first step towards adapting modulation spaces to the magnetic case.


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Additional Information

Marius Mantoiu
Affiliation: Departamento de Matematicas, Universidad de Chile, Las Palmeras 3425, Casilla 653, Santiago, Chile
Email: Marius.Mantoiu@imar.ro, mantoiu@uchile.cl

Radu Purice
Affiliation: Institute of Mathematics Simion Stoilow of the Romanian Academy, P.O. Box 1-764, Bucharest, RO-70700, Romania
Email: Radu.Purice@imar.ro

DOI: https://doi.org/10.1090/S0002-9939-10-10345-1
Keywords: Magnetic field, pseudodifferential operator, phase space, modulation mapping, crossed product algebra, coherent states, Bargmann transform
Received by editor(s): July 30, 2009
Received by editor(s) in revised form: December 2, 2009
Published electronically: April 2, 2010
Additional Notes: The first author is partially supported by Núcleo Cientifico ICM P07-027-F “Mathematical Theory of Quantum and Classical Magnetic Systems” and by the Chilean Science Foundation Fondecyt under grant no. 1085162. His interest in modulation spaces was raised by a very enjoyable visit to the University of Vienna in February 2009.
The second author acknowledges partial support from contract no. 2-CEx 06-11-18/2006.
Communicated by: Marius Junge
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.