A $q$-deformation of true-polyanalytic Bargmann transforms when $q^{-1}>1$

Othmane El Moize; Zouhaïr Mouayn

doi:10.5802/crmath.284

Mathematical physics

A

q

-deformation of true-polyanalytic Bargmann transforms when

q^{- 1} > 1

Othmane El Moize ¹; Zouhaïr Mouayn ^2,³

¹ Department of Mathematics, Faculty of Sciences, Ibn Tofaïl University, P.O. Box. 133, Kénitra, Morocco
² Department of Mathematics, Faculty of Sciences and Technics (M’Ghila), Sultan Moulay Slimane University, P.O. Box. 523, Béni Mellal, Morocco
³ Department of Mathematics, KTH Royal Institute of Technology, SE-10044, Stockholm, Sweden

Comptes Rendus. Mathématique, Volume 359 (2021) no. 10, pp. 1295-1305.

Abstract

We combine continuous $q^{- 1}$ -Hermite Askey polynomials with new $2 D$ 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 Arïk-Coon oscillator for $q^{'} = q^{- 1} > 1$ . These result may be used to introduce a $q$ -deformed Ginibre-type point process.

Received: 2020-07-23
Accepted: 2021-10-13
Published online: 2022-01-04

DOI: 10.5802/crmath.284

Author's affiliations:

Othmane El Moize ¹; Zouhaïr Mouayn ^{2, 3}

¹ Department of Mathematics, Faculty of Sciences, Ibn Tofaïl University, P.O. Box. 133, Kénitra, Morocco
² Department of Mathematics, Faculty of Sciences and Technics (M’Ghila), Sultan Moulay Slimane University, P.O. Box. 523, Béni Mellal, Morocco
³ Department of Mathematics, KTH Royal Institute of Technology, SE-10044, Stockholm, Sweden

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     author = {Othmane El Moize and Zouha{\"\i}r Mouayn},
     title = {A $q$-deformation of true-polyanalytic {Bargmann} transforms when $q^{-1}>1$},
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Othmane El Moize; Zouhaïr Mouayn. A $q$-deformation of true-polyanalytic Bargmann transforms when $q^{-1}>1$. Comptes Rendus. Mathématique, Volume 359 (2021) no. 10, pp. 1295-1305. doi : 10.5802/crmath.284. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.284/

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