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}, eid = {2}, pages = {1--13}, publisher = {Groupement de recherche 2434 du CNRS}, year = {2004}, doi = {10.5802/jedp.2}, zbl = {1067.35082}, mrnumber = {2135357}, language = {en}, url = {http://www.numdam.org/articles/10.5802/jedp.2/} }
TY - JOUR AU - Ammari, Zied TI - Canonical commutation relations and interacting Fock spaces JO - Journées équations aux dérivées partielles PY - 2004 SP - 1 EP - 13 PB - Groupement de recherche 2434 du CNRS UR - http://www.numdam.org/articles/10.5802/jedp.2/ DO - 10.5802/jedp.2 LA - en ID - JEDP_2004____A2_0 ER -
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/articles/10.5802/jedp.2/
[Am] Ammari, Z.: On canonical commutation relations and quantization in infinite dimension spaces, in preparation
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