### Some remarks on Weyl pseudodifferential operators

Jan Derezinski (1993)

Journées équations aux dérivées partielles

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Jan Derezinski (1993)

Journées équations aux dérivées partielles

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Ruffing, Andreas (2000)

Discrete Dynamics in Nature and Society

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A. Voros (1977)

Annales de l'I.H.P. Physique théorique

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Luigi Barletti (2003)

Bollettino dell'Unione Matematica Italiana

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The paper is devoted to review, from a mathematical point of view, some fundamental aspects of the Wigner formulation of quantum mechanics. Starting from the axioms of quantum mechanics and of quantum statistics, we justify the introduction of the Wigner transform and eventually deduce the Wigner equation.

Ruffing, Andreas (2000)

Discrete Dynamics in Nature and Society

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Zied Ammari (2004)

Journées Équations aux dérivées partielles

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We introduce by means of reproducing kernel theory and decomposition in orthogonal polynomials canonical correspondences between an interacting Fock space a reproducing kernel Hilbert space and a square integrable functions space w.r.t. a cylindrical measure. Using this correspondences we investigate the structure of the infinite dimensional canonical commutation relations. In particular we construct test functions spaces, distributions spaces and a quantization map which generalized...