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Wick calculus for noncommutative white noise corresponding to $q$-deformed commutation relations
- Publication Year :
- 2016
-
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.
- Subjects :
- Mathematics - Probability
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1608.00211
- Document Type :
- Working Paper