Maximal covariance group of Wigner transforms and pseudo-differential operators

Dias, Nuno; de Gosson, Maurice; Prata, João

doi:10.1090/S0002-9939-2014-12311-2

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.

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