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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
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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...
| Published in: | Complex Analysis and Operator Theory |
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| ISSN: | 1661-8254 1661-8262 |
| Published: |
2017
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| Online Access: |
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| 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. |
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| Keywords: |
q-commutation relations, noncommutative white noise, q-white noise, Wick product, Wick-power series |
| College: |
Faculty of Science and Engineering |