Wick Calculus for Noncommutative White Noise Corresponding to q-Deformed Commutation Relations

摘要

We derive the Wick calculus for test and generalized functionals of noncommutative white noise corresponding to q-deformed commutation relations with q is an element of (-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.