Maximal covariance group of Wigner transforms and pseudo-differential operators
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- by Nuno Costa Dias, Maurice A. de Gosson and João Nuno Prata PDF
- Proc. Amer. Math. Soc. 142 (2014), 3183-3192 Request permission
Abstract:
We show that the linear symplectic and antisymplectic transformations form the maximal covariance group for both the Wigner transform and Weyl operators. The proof is based on a new result from symplectic geometry which characterizes symplectic and antisymplectic matrices and which allows us, in addition, to refine a classical result on the preservation of symplectic capacities of ellipsoids.References
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Additional Information
- Nuno Costa Dias
- Affiliation: Departamento de Matemática, Universidade Lusófona, Av. Campo Grande, 376, 1749-024 Lisboa, Portugal
- Email: ncdias@meo.pt
- Maurice A. de Gosson
- Affiliation: Faculty of Mathematics, NuHAG, University of Vienna, Nordbergstrasse 15, A-1090 Vienna, Austria
- MR Author ID: 189618
- Email: maurice.de.gosson@univie.ac.at
- João Nuno Prata
- Affiliation: Departamento de Matemática, Universidade Lusófona, Av. Campo Grande, 376, 1749-024 Lisboa, Portugal
- Email: joao.prata@mail.telepac.pt
- Received by editor(s): October 7, 2012
- Published electronically: June 3, 2014
- Additional Notes: The first author was supported by a research grant from the Austrian Research Agency FWF (Projektnummer P23902-N13)
The second and third authors were supported by the research grant PTDC/MAT/099880/2008 of the Portuguese Science Foundation - Communicated by: Alexander Iosevich
- © Copyright 2014 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 142 (2014), 3183-3192
- MSC (2010): Primary 35S99, 35P05, 53D05; Secondary 35S05
- DOI: https://doi.org/10.1090/S0002-9939-2014-12311-2
- MathSciNet review: 3223374