Wick Calculus for Noncommutative White Noise Corresponding to q-Deformed Commutation Relations - Eugene Lytvynov (Complex Analysis and Operator Theory, 2017)
We derive the Wick calculus for test and generalized functionals of noncommutative white noise corresponding to q-deformed commutation relations with $q\in(-1,1)$.We construct a Gel'fand triple centered at the q-deformed Fock space in which both the test, nuclear space and its dual space are algebras with respect to the addition and the Wick multiplication. Furthermore, we prove a Vage-type inequality for the Wick product on the dual space.