Displaying similar documents to “Integral representations and coherent states.”

Dichotomies for 𝐂 0 ( X ) and 𝐂 b ( X ) spaces

Szymon Głąb, Filip Strobin (2013)

Czechoslovak Mathematical Journal

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Jachymski showed that the set ( x , y ) ∈ 𝐜 0 × 𝐜 0 : ∑ i = 1 n α ( i ) x ( i ) y ( i ) n = 1 ∞ is bounded is either a meager subset of 𝐜 0 × 𝐜 0 or is equal to 𝐜 0 × 𝐜 0 . In the paper we generalize this result by considering more general spaces than 𝐜 0 , namely 𝐂 0 ( X ) , the space of all continuous functions which vanish at infinity, and 𝐂 b ( X ) , the space of all continuous bounded functions. Moreover, we replace the meagerness by σ -porosity.

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...