No Cover Image

Journal article 1520 views 196 downloads

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

Check full text

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...

Full description

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
first_indexed 2017-01-05T14:48:47Z
last_indexed 2018-02-09T05:18:39Z
id cronfa31576
recordtype SURis
fullrecord <?xml version="1.0"?><rfc1807><datestamp>2017-02-03T18:08:50.6560570</datestamp><bib-version>v2</bib-version><id>31576</id><entry>2017-01-05</entry><title>Wick Calculus for Noncommutative White Noise Corresponding to q-Deformed Commutation Relations</title><swanseaauthors><author><sid>e5b4fef159d90a480b1961cef89a17b7</sid><ORCID>0000-0001-9685-7727</ORCID><firstname>Eugene</firstname><surname>Lytvynov</surname><name>Eugene Lytvynov</name><active>true</active><ethesisStudent>false</ethesisStudent></author></swanseaauthors><date>2017-01-05</date><deptcode>MACS</deptcode><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.</abstract><type>Journal Article</type><journal>Complex Analysis and Operator Theory</journal><publisher/><issnPrint>1661-8254</issnPrint><issnElectronic>1661-8262</issnElectronic><keywords>q-commutation relations, noncommutative white noise, q-white noise, Wick product, Wick-power series</keywords><publishedDay>31</publishedDay><publishedMonth>12</publishedMonth><publishedYear>2017</publishedYear><publishedDate>2017-12-31</publishedDate><doi>10.1007/s11785-016-0635-3</doi><url/><notes/><college>COLLEGE NANME</college><department>Mathematics and Computer Science School</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>MACS</DepartmentCode><institution>Swansea University</institution><apcterm/><lastEdited>2017-02-03T18:08:50.6560570</lastEdited><Created>2017-01-05T12:34:12.5185578</Created><path><level id="1">Faculty of Science and Engineering</level><level id="2">School of Mathematics and Computer Science - Mathematics</level></path><authors><author><firstname>Un Cig</firstname><surname>Ji</surname><order>1</order></author><author><firstname>Eugene</firstname><surname>Lytvynov</surname><orcid>0000-0001-9685-7727</orcid><order>2</order></author></authors><documents><document><filename>0031576-05012017134647.pdf</filename><originalFilename>Ji-Lytvynov-CAOT.pdf</originalFilename><uploaded>2017-01-05T13:46:47.0700000</uploaded><type>Output</type><contentLength>366304</contentLength><contentType>application/pdf</contentType><version>Accepted Manuscript</version><cronfaStatus>true</cronfaStatus><embargoDate>2018-01-03T00:00:00.0000000</embargoDate><copyrightCorrect>true</copyrightCorrect></document></documents><OutputDurs/></rfc1807>
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
hierarchytype
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
active_str 0
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 2017-12-31T13:08:47Z
_version_ 1821411039371067392
score 11.247077

Similar Items