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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: Eugene Lytvynov

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
ISSN: 1661-8254 1661-8262
Published: 2017
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa31576
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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.
Keywords: q-commutation relations, noncommutative white noise, q-white noise, Wick product, Wick-power series
College: College of Science