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Journal of the London Mathematical Society Advance Access published online on June 26, 2008
Journal of the London Mathematical Society, doi:10.1112/jlms/jdn036
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© 2008 London Mathematical Society

Ultrarapidly decreasing ultradifferentiable functions, Wigner distributions and density matrices

Jean-Marie Aubry

Université Paris-Est
LAMA – UMR CNRS 8050
94010 Créteil
France

Spaces S{omega}, SFormula , SFormula of ultradecreasing ultradifferentiable (or for short, ultra-S) functions, depending on a weight e{omega}(x), are introduced in the context of quantum statistics. The corresponding coefficient spaces in the Fock basis are identified, and it is shown that the Hermite expansion is a tame isomorphism between these spaces. These results are used to link decay properties of density matrices to corresponding properties of the Wigner distribution.

2000 Mathematics Subject Classification 46A61 (primary), 33C45, 46A13 (secondary).

The author acknowledges the support of the French Agence Nationale de la Recherche (ANR), under grant StatQuant (JCJC07 205763) ‘Quantum Statistics’.

Received April 11, 2007; revised October 2, 2007;
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