Ultrarapidly decreasing ultradifferentiable functions, Wigner distributions and density matrices
Jean-Marie Aubry
Spaces S ω , S { ϖ } , S { ϖ } of ultradecreasing ultradifferentiable (or for short, ultra-𝒮) functions, depending on a weight eω(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.
arXiv:math/0703884•Journal of the London Mathematical Society•Jun 26, 2008•4 citations