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arXiv · 1608.00211

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

Un Cig Ji·Eugene Lytvynov
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Abstract

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 V\r{a}ge-type inequality for the Wick product on the dual space.

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Un Cig Ji, Eugene Lytvynov. 2016-07-31. Wick calculus for noncommutative white noise corresponding to $q$-deformed commutation relations. https://arxiv.org/abs/1608.00211

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