English

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

Probability 2016-12-16 v2

Abstract

We derive the Wick calculus for test and generalized functionals of noncommutative white noise corresponding to qq-deformed commutation relations with q(1,1)q\in(-1,1). We construct a Gel'fand triple centered at the qq-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.

Keywords

Cite

@article{arxiv.1608.00211,
  title  = {Wick calculus for noncommutative white noise corresponding to $q$-deformed commutation relations},
  author = {Un Cig Ji and Eugene Lytvynov},
  journal= {arXiv preprint arXiv:1608.00211},
  year   = {2016}
}
R2 v1 2026-06-22T15:08:34.250Z