Canonical commutation relations and interacting Fock spaces
Journées équations aux dérivées partielles (2004), article no. 2, 13 p.

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 the work of Krée-Rączka [KR] and Janas-Rudol [JR1]-[JR3].

@article{JEDP_2004____A2_0,
     author = {Ammari, Zied},
     title = {Canonical commutation relations and interacting Fock spaces},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     publisher = {Groupement de recherche 2434 du CNRS},
     year = {2004},
     doi = {10.5802/jedp.2},
     mrnumber = {2135357},
     zbl = {1067.35082},
     language = {en},
     url = {http://www.numdam.org/item/JEDP_2004____A2_0}
}
Ammari, Zied. Canonical commutation relations and interacting Fock spaces. Journées équations aux dérivées partielles (2004), article  no. 2, 13 p. doi : 10.5802/jedp.2. http://www.numdam.org/item/JEDP_2004____A2_0/

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