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Ultrarapidly decreasing ultradifferentiable functions, Wigner distributions and density matrices

Jean-Marie Aubry
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Abstract

Spaces $S_ω, S_{\{ω\}}, S_{(ω)}$ of ultradecreasing ultradifferentiable (or for short, ultra-S) functions, depending on a weight $e^{ω(x)}$, 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 decrease properties of density matrices to corresponding properties of the Wigner distribution.

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Jean-Marie Aubry. 2008-05-20. Ultrarapidly decreasing ultradifferentiable functions, Wigner distributions and density matrices. https://doi.org/10.1112/jlms%2Fjdn036

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