Resumen de Ultrarapidly decreasing ultradifferentiable functions, Wigner distributions and density matrices

Jean-Marie Aubry

• Spaces , , of ultradecreasing ultradifferentiable (or for short, ultra-) functions, depending on a weight e(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