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Ultrarapidly decreasing ultradifferentiable functions, Wigner distributions and density matrices

Abstract : Spaces S(omega), S{(omega) over bar}, S((omega) over bar) 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.
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Jean-Marie Aubry. Ultrarapidly decreasing ultradifferentiable functions, Wigner distributions and density matrices. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2008, 78 (?), pp.392--406. ⟨10.1112/jlms/jdn036⟩. ⟨hal-00693061⟩

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