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  • 1. Gosson, Maurice de
    Symplectic quantam cells and Wigner and Husimi functions2005In: Bulletin des Sciences Mathématiques, ISSN 0007-4497, E-ISSN 1952-4773, Vol. 129, no 3, p. 211-226Article in journal (Refereed)
    Abstract [en]

    We propose a definition of quantum cells which is invariant under symplectic transformations. We use this notion to the study of positivity properties of the Wigner and Husimi functions, which allows us to precise and to improve known results. © 2004 Elsevier SAS. Tous droits réservés.

  • 2. Toft, Joachim
    Continuity properties in non-commutative convolution algebras, with applications in pseudo-differential calculus2002In: Bulletin des Sciences Mathématiques, ISSN 0007-4497, E-ISSN 1952-4773, Vol. 126, no 2, p. 115-142Article in journal (Refereed)
    Abstract [en]

    We study continuity properties for a family {s(p)} p greater than or equal to 1 of increasing Banach algebras under the twisted convolution, which also satisfies that a is an element of s(p), if and only if the Weyl operator a(w) (x, D) is a Schatten-von Neumann operator of order p on L-2. We discuss inclusion relations between the s(p)-spaces, Besov spaces and Sobolev spaces. We prove also a Young type result on sp for dilated convolution. As an application we prove that f (a) is an element of s(1), when a is an element of s(1) and f is an entire odd function. We finally apply the results on Toeplitz operators and prove that we may extend the definition for such operators. (C) 2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved.

  • 3. Toft, Joachim
    Positivity properties in noncommutative convolution algebras with applications in pseudo-differential calculus2003In: Bulletin des Sciences Mathématiques, ISSN 0007-4497, E-ISSN 1952-4773, p. 101-132Article in journal (Refereed)
    Abstract [en]

    We study Y'(+), of all a is an element of D' such that (a *sigma, phi, phi) greater than or equal to 0 for every phi is an element of C-0(infinity), where *phi denotes the twisted convolution. We prove that certain boundedness for a E Y' are completely determined of the behaviour for a at origin, for example that a is an element of Y'(+), and that if a(0) < &INFIN;, then a &ISIN; L-2 &AND; L-&INFIN;. We use the results in order to determine wether positive pseudo-differential operators belong to certain Schatten-casses or not. (C) 2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved.

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