Ultrarapidly decreasing ultradifferentiable functions, Wigner distributions and density matrices

Details Ultrarapidly decreasing ultradifferentiable functions, Wigner distributions and density matrices Ultrarapidly decreasing ultradifferentiable functions, Wigner distributions and density matrices

2007-03-29

arxiv.org/abs/math/0703884v2

Mathematics

Functional Analysis

Scientific paper

Spaces $S_{\omega}, S_{\{\omega\}}, S_{(\omega)}$ 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 decrease properties of density matrices to corresponding properties of the Wigner distribution.

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