An Analytic Characterization of p,q-White Noise Functionals
In this paper, a characterization theorem for the S-transform of infinite dimensional distributions of noncommutative white noise corresponding to the p,q-deformed quantum oscillator algebra is investigated. We derive a unitary operator U between the noncommutative L2-space and the p,q-Fock space wh...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/6319138 |
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| _version_ | 1850177675443830784 |
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| author | Anis Riahi Amine Ettaieb Wathek Chammam Ziyad Ali Alhussain |
| author_facet | Anis Riahi Amine Ettaieb Wathek Chammam Ziyad Ali Alhussain |
| author_sort | Anis Riahi |
| collection | DOAJ |
| description | In this paper, a characterization theorem for the S-transform of infinite dimensional distributions of noncommutative white noise corresponding to the p,q-deformed quantum oscillator algebra is investigated. We derive a unitary operator U between the noncommutative L2-space and the p,q-Fock space which serves to give the construction of a white noise Gel’fand triple. Next, a general characterization theorem is proven for the space of p,q-Gaussian white noise distributions in terms of new spaces of p,q-entire functions with certain growth rates determined by Young functions and a suitable p,q-exponential map. |
| format | Article |
| id | doaj-art-c36c840b722d48a29dc32ee68ab2f9cc |
| institution | OA Journals |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-c36c840b722d48a29dc32ee68ab2f9cc2025-08-20T02:18:55ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/63191386319138An Analytic Characterization of p,q-White Noise FunctionalsAnis Riahi0Amine Ettaieb1Wathek Chammam2Ziyad Ali Alhussain3Department of Mathematics, College of Science Al-Zulfi, Majmaah University, P.O. Box 66, Al-Majmaah 11952, Saudi ArabiaDepartment of Mathematics, Higher School of Sciences and Technologies of Hammam-Sousse, MaPSFA Laboratory, Sousse University, Hammam Sousse 4011, TunisiaDepartment of Mathematics, College of Science Al-Zulfi, Majmaah University, P.O. Box 66, Al-Majmaah 11952, Saudi ArabiaDepartment of Mathematics, College of Science Al-Zulfi, Majmaah University, P.O. Box 66, Al-Majmaah 11952, Saudi ArabiaIn this paper, a characterization theorem for the S-transform of infinite dimensional distributions of noncommutative white noise corresponding to the p,q-deformed quantum oscillator algebra is investigated. We derive a unitary operator U between the noncommutative L2-space and the p,q-Fock space which serves to give the construction of a white noise Gel’fand triple. Next, a general characterization theorem is proven for the space of p,q-Gaussian white noise distributions in terms of new spaces of p,q-entire functions with certain growth rates determined by Young functions and a suitable p,q-exponential map.http://dx.doi.org/10.1155/2020/6319138 |
| spellingShingle | Anis Riahi Amine Ettaieb Wathek Chammam Ziyad Ali Alhussain An Analytic Characterization of p,q-White Noise Functionals Journal of Mathematics |
| title | An Analytic Characterization of p,q-White Noise Functionals |
| title_full | An Analytic Characterization of p,q-White Noise Functionals |
| title_fullStr | An Analytic Characterization of p,q-White Noise Functionals |
| title_full_unstemmed | An Analytic Characterization of p,q-White Noise Functionals |
| title_short | An Analytic Characterization of p,q-White Noise Functionals |
| title_sort | analytic characterization of p q white noise functionals |
| url | http://dx.doi.org/10.1155/2020/6319138 |
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