Mathematical physics
A q-deformation of true-polyanalytic Bargmann transforms when q -1 >1
Comptes Rendus. Mathématique, Volume 359 (2021) no. 10, pp. 1295-1305.

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 Arïk-Coon oscillator for q =q -1 >1. These result may be used to introduce a q-deformed Ginibre-type point process.

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DOI: 10.5802/crmath.284
El Moize, Othmane 1; Mouayn, Zouhaïr 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
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El Moize, Othmane; Mouayn, Zouhaïr. 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. http://www.numdam.org/articles/10.5802/crmath.284/

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