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Displaying similar documents to “Canonical commutation relations and interacting Fock spaces”

An algebra of pseudo-differential operators and quantum mechanics in phase space

A. Grossmann, Guy Loupias, Elias M. Stein (1968)

Annales de l'institut Fourier

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Nous étudions une algèbre 𝒫 de fonctions infiniment différentiables définies sur l’espace de phase et satisfaisant des conditions de croissance à l’infini. Le produit dans 𝒫 est la transformée de Fourier symplectique de la convolution gauche. On montre que 𝒫 est une généralisation naturelle de l’algèbre des opérateurs pseudodifférentiels.

Fourier analysis of a space of Hilbert-Shmidt operators. New type operators.

Jaak Peetre (1990)

Publicacions Matemàtiques

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If a group acts via unitary operators on a Hilbert space of functions then this group action extends in an obvious way to the space of Hilbert-Schmidt operators over the given Hilbert space. Even if the action on functions is irreducible, the action on H.-S. operators need not be irreducible. It is often of considerable interest to find out what the irreducible constituents are. Such an attitude has recently been advocated in the theory of "Ha-pliz" (Hankel + Toeplitz) operators. In...

Integral representations of unbounded operators by infinitely smooth kernels

Igor Novitskiî (2005)

Open Mathematics

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In this paper, we prove that every unbounded linear operator satisfying the Korotkov-Weidmann characterization is unitarily equivalent to an integral operator in L 2(R), with a bounded and infinitely smooth Carleman kernel. The established unitary equivalence is implemented by explicitly definable unitary operators.