### Wick Calculus for Noncommutative White Noise Corresponding to q-Deformed Commutation Relations / Un Cig Ji, Eugene Lytvynov

Complex Analysis and Operator Theory

Swansea University Author:

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DOI (Published version): 10.1007/s11785-016-0635-3

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 al...

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Published in: Complex Analysis and Operator Theory 1661-8254 1661-8262 2017 https://cronfa.swan.ac.uk/Record/cronfa31576 No Tags, Be the first to tag this record!
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 Vage-type inequality for the Wick product on the dual space. q-commutation relations, noncommutative white noise, q-white noise, Wick product, Wick-power series College of Science