Displaying similar documents to “Certain function spaces related to the metaplectic representation”

Local Toeplitz operators based on wavelets: phase space patterns for rough wavelets

Krzysztof Nowak (1996)

Studia Mathematica

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We consider two standard group representations: one acting on functions by translations and dilations, the other by translations and modulations, and we study local Toeplitz operators based on them. Local Toeplitz operators are the averages of projection-valued functions g ↦ P g , ϕ , where for a fixed function ϕ, P g , ϕ denotes the one-dimensional orthogonal projection on the function U g ϕ , U is a group representation and g is an element of the group. They are defined as integrals ʃ W P g , ϕ d g , where W is an open,...

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.

Canonical commutation relations and interacting Fock spaces

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...

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.