English

Ultrarapidly decreasing ultradifferentiable functions, Wigner distributions and density matrices

Functional Analysis 2014-02-26 v2 Mathematical Physics math.MP

Abstract

Spaces Sω,S{ω},S(ω)S_{\omega}, S_{\{\omega\}}, S_{(\omega)} of ultradecreasing ultradifferentiable (or for short, ultra-S) functions, depending on a weight eω(x)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.

Keywords

Cite

@article{arxiv.math/0703884,
  title  = {Ultrarapidly decreasing ultradifferentiable functions, Wigner distributions and density matrices},
  author = {Jean-Marie Aubry},
  journal= {arXiv preprint arXiv:math/0703884},
  year   = {2014}
}
R2 v1 2026-07-22T17:53:27.620Z