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A q-deformation of true-polyanalytic Bargmann transforms when q(-1) > 1
Ibn Tofail Univ, Fac Sci, Dept Math, POB 133, Kenitra, Morocco..
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). Sultan Moulay Slimane Univ, Fac Sci & Tech MGhila, Dept Math, POB 523, Beni Mellal, Morocco..
2021 (English)In: Comptes rendus. Mathematique, ISSN 1631-073X, E-ISSN 1778-3569, Vol. 359, no 10, p. 1295-1305Article in journal (Refereed) Published
Abstract [en]

We combine continuous q(-1)-Hermite Askey polynomials with new 2D orthogonal polynomials introduced by Ismail and Zhang as q-analogs for complex Hermite polynomials to construct a new set of coherent states depending on a nonnegative integer parameter m. Our construction leads to a new q-deformation of the m-true- polyanalytic Bargmann transform on the complex plane. In the analytic case m = 0, the obtained coherent states transform can be associated with the Arik-Coon oscillator for q(0) = q(-1) > 1. These result may be used to introduce a q-deformed Ginibre-type point process.

Place, publisher, year, edition, pages
Cellule MathDoc/CEDRAM , 2021. Vol. 359, no 10, p. 1295-1305
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:kth:diva-307273DOI: 10.5802/crmath.284ISI: 000740810200008Scopus ID: 2-s2.0-85123361213OAI: oai:DiVA.org:kth-307273DiVA, id: diva2:1630378
Note

QC 20220120

Available from: 2022-01-20 Created: 2022-01-20 Last updated: 2022-06-25Bibliographically approved

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Mouayn, Zouhair

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