Complex Analysis and Operator Theory

, Volume 12, Issue 7, pp 1497–1517 | Cite as

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

  • Un Cig JiEmail author
  • Eugene Lytvynov


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.


q-commutation relations Noncommutative white noise q-white noise Wick product Wick-power series 

Mathematics Subject Classification

Primary 60H40 Secondary 46A11 46L53 



We would like to thank the anonymous referee for their careful reading of our manuscript and bringing the paper [2] to our attention.


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Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  1. 1.Department of MathematicsChungbuk National UniversityCheongjuRepublic of Korea
  2. 2.Department of MathematicsSwansea UniversitySwanseaUK

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