Ultrarapidly decreasing ultradifferentiable functions, Wigner distributions and density matrices

• Autores: Jean-Marie Aubry
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 78, Nº 2, 2008, págs. 392-406
• Idioma: inglés
• DOI: 10.1112/jlms/jdn036
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• Resumen

  • 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