Wick Calculus for Noncommutative White Noise Corresponding to q-Deformed Commutation Relations
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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 Våge-type inequality for the Wick product on the dual space.
Keywordsq-commutation relations Noncommutative white noise q-white noise Wick product Wick-power series
Mathematics Subject ClassificationPrimary 60H40 Secondary 46A11 46L53
We would like to thank the anonymous referee for their careful reading of our manuscript and bringing the paper  to our attention.
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