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Ultrarapidly decreasing ultradifferentiable functions, Wigner distributions and density matrices
Author(s) -
Aubry Jean-Marie
Publication year - 2008
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdn036
Subject(s) - isomorphism (crystallography) , context (archaeology) , fock space , wigner distribution function , hermite polynomials , basis (linear algebra) , mathematics , pure mathematics , quantum , distribution (mathematics) , physics , quantum mechanics , mathematical analysis , chemistry , geometry , geology , crystallography , crystal structure , paleontology
SpacesS ω , S { ϖ } , S { ϖ }of ultradecreasing ultradifferentiable (or for short, ultra‐) functions, depending on a weight e ω( 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.