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Wick Calculus for Noncommutative White Noise Corresponding to q-Deformed Commutation Relations

Un Cig Ji, Eugene Lytvynov Orcid Logo

Complex Analysis and Operator Theory

Swansea University Author: Eugene Lytvynov Orcid Logo

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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
ISSN: 1661-8254 1661-8262
Published: 2017
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URI: https://cronfa.swan.ac.uk/Record/cronfa31576
first_indexed 2017-01-05T14:48:47Z
last_indexed 2018-02-09T05:18:39Z
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spelling 2017-02-03T18:08:50.6560570 v2 31576 2017-01-05 Wick Calculus for Noncommutative White Noise Corresponding to q-Deformed Commutation Relations e5b4fef159d90a480b1961cef89a17b7 0000-0001-9685-7727 Eugene Lytvynov Eugene Lytvynov true false 2017-01-05 MACS 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. Journal Article Complex Analysis and Operator Theory 1661-8254 1661-8262 q-commutation relations, noncommutative white noise, q-white noise, Wick product, Wick-power series 31 12 2017 2017-12-31 10.1007/s11785-016-0635-3 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University 2017-02-03T18:08:50.6560570 2017-01-05T12:34:12.5185578 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Un Cig Ji 1 Eugene Lytvynov 0000-0001-9685-7727 2 0031576-05012017134647.pdf Ji-Lytvynov-CAOT.pdf 2017-01-05T13:46:47.0700000 Output 366304 application/pdf Accepted Manuscript true 2018-01-03T00:00:00.0000000 true
title Wick Calculus for Noncommutative White Noise Corresponding to q-Deformed Commutation Relations
spellingShingle Wick Calculus for Noncommutative White Noise Corresponding to q-Deformed Commutation Relations
Eugene Lytvynov
title_short Wick Calculus for Noncommutative White Noise Corresponding to q-Deformed Commutation Relations
title_full Wick Calculus for Noncommutative White Noise Corresponding to q-Deformed Commutation Relations
title_fullStr Wick Calculus for Noncommutative White Noise Corresponding to q-Deformed Commutation Relations
title_full_unstemmed Wick Calculus for Noncommutative White Noise Corresponding to q-Deformed Commutation Relations
title_sort Wick Calculus for Noncommutative White Noise Corresponding to q-Deformed Commutation Relations
author_id_str_mv e5b4fef159d90a480b1961cef89a17b7
author_id_fullname_str_mv e5b4fef159d90a480b1961cef89a17b7_***_Eugene Lytvynov
author Eugene Lytvynov
author2 Un Cig Ji
Eugene Lytvynov
format Journal article
container_title Complex Analysis and Operator Theory
publishDate 2017
institution Swansea University
issn 1661-8254
1661-8262
doi_str_mv 10.1007/s11785-016-0635-3
college_str Faculty of Science and Engineering
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hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
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description 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.
published_date 2017-12-31T04:01:42Z
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score 11.089407

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