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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 Ji
  • Eugene Lytvynov
Article
  • 61 Downloads

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 Våge-type inequality for the Wick product on the dual space.

Keywords

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

Mathematics Subject Classification

Primary 60H40 Secondary 46A11 46L53 

Notes

Acknowledgements

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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