Wick calculus for noncommutative white noise corresponding to $q$-deformed commutation relations

摘要

We derive the Wick calculus for test and generalized functionals ofnoncommutative white noise corresponding to $q$-deformed commutation relationswith $q\in(-1,1)$. We construct a Gel'fand triple centered at the $q$-deformedFock space in which both the test, nuclear space and its dual space arealgebras with respect to the addition and the Wick multiplication. Furthermore,we prove a V\r{a}ge-type inequality for the Wick product on the dual space.