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 -deformed commutation relations with . We construct a Gel'fand triple centered at the -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}
}