Physique mathématique
Une q-déformation de la transformation de Bargmann vraie-polyanalytique
[A q-deformation of the true-polyanalytic Bargmann transform]
Comptes Rendus. Mathématique, Volume 356 (2018) no. 8, pp. 903-910.

We introduce a q-analog of the true-polyanalytic Bargmann transform on C.

Nous introduisons une version q-deformée de la transformation de Bargmann vraie-polyanalytique sur C.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2018.05.017
Arjika, Sama 1; El Moize, Othmane 2; Mouayn, Zouhaïr 3

1 Department of Mathematics and Computer Sciences, Faculty of Sciences and Technics, University of Agadez, BP 199, Agadez, Niger
2 Department of Mathematics, Faculty of Sciences, BP 133, Kénitra, Maroc
3 Department of Mathematics, Faculty of Sciences and Technics (M'Ghila), BP 523, Béni Mellal, Maroc
@article{CRMATH_2018__356_8_903_0,
     author = {Arjika, Sama and El Moize, Othmane and Mouayn, Zouha{\"\i}r},
     title = {Une \protect\emph{q}-d\'eformation de la transformation de {Bargmann} vraie-polyanalytique},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {903--910},
     publisher = {Elsevier},
     volume = {356},
     number = {8},
     year = {2018},
     doi = {10.1016/j.crma.2018.05.017},
     language = {fr},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2018.05.017/}
}
TY  - JOUR
AU  - Arjika, Sama
AU  - El Moize, Othmane
AU  - Mouayn, Zouhaïr
TI  - Une q-déformation de la transformation de Bargmann vraie-polyanalytique
JO  - Comptes Rendus. Mathématique
PY  - 2018
SP  - 903
EP  - 910
VL  - 356
IS  - 8
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2018.05.017/
DO  - 10.1016/j.crma.2018.05.017
LA  - fr
ID  - CRMATH_2018__356_8_903_0
ER  - 
%0 Journal Article
%A Arjika, Sama
%A El Moize, Othmane
%A Mouayn, Zouhaïr
%T Une q-déformation de la transformation de Bargmann vraie-polyanalytique
%J Comptes Rendus. Mathématique
%D 2018
%P 903-910
%V 356
%N 8
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2018.05.017/
%R 10.1016/j.crma.2018.05.017
%G fr
%F CRMATH_2018__356_8_903_0
Arjika, Sama; El Moize, Othmane; Mouayn, Zouhaïr. Une q-déformation de la transformation de Bargmann vraie-polyanalytique. Comptes Rendus. Mathématique, Volume 356 (2018) no. 8, pp. 903-910. doi : 10.1016/j.crma.2018.05.017. http://www.numdam.org/articles/10.1016/j.crma.2018.05.017/

[1] Abreu, L.D. Sampling and interpolation in Bargmann–Fock spaces of polyanalytic functions, Appl. Comput. Harmon. Anal., Volume 29 (2010), pp. 287-302

[2] Abreu, L.D.; Feichtinger, H.G. Function spaces of polyanalytic functions, Harmonic and Complex Analysis and Its Application, Birkhäuser, 2014, pp. 1-38

[3] Abreu, L.D.; Balazs, P.; de Gosson, M.; Mouayn, Z. Discrete coherent states for higher Landau levels, Ann. Phys., Volume 363 (2015), pp. 337-353

[4] Arik, M.; Coon, D.D. Hilbert space of analytic function and generalized coherent states, J. Math. Phys., Volume 17 (1976) no. 4, pp. 524-527

[5] Aronszajn, N. Theory of reproducing kernels, Trans. Amer. Math. Soc., Volume 68 (1950), pp. 337-404

[6] Askour, N.; Intissar, A.; Mouayn, Z. Espaces de Bargmann généralisés et formules explicites pour leurs noyaux reproduisants, C. R. Acad. Sci. Paris, Ser. I, Volume 325 (1997) no. 7, pp. 707-712

[7] Bargmann, V. On a Hilbert space of analytic functions and an associated integral transform, Part I, Commun. Pure Appl. Math., Volume 14 (1961), pp. 174-187

[8] Folland, G.B. Harmonic Analyse on Phase Space, vol. 122, Princeton University Press, Princeton, NJ, États-Unis, 1989 (x+277 p)

[9] Gasper, G.; Rahman, M. Basic Hypergeometric Series, Encyclopedia of Mathematics and Its Applications, vol. 96, Cambridge University Press, Cambridge, Royaume-Uni, 2004

[10] Gazeau, J.P. Coherent States in Quantum Physics, Wiley-VCH, Weinheim, Allemagne, 2009

[11] Hall, B.C. Bounds on the Segal–Bargmann transform of Lp functions, J. Fourier Anal. Appl., Volume 7 (2001) no. 6, pp. 553-569

[12] Ismail, M.E.H.; Zhang, R. On some 2D orthogonal q-polynomials, Trans. Amer. Math. Soc., Volume 369 (2017) no. 10, pp. 6779-6821

[13] Ismail, M.E.H.; Dennis, S.; Gérard, V. The combinatorics of q-Hermite polynomials and the Askey–Wilson integral, Eur. J. Comb., Volume 8 (1987) no. 4, pp. 379-392

[14] Itô, K. Complex multiple Wiener integral, Jpn. J. Math., Volume 22 (1952), pp. 63-86

[15] Koekoek, R.; Swarttouw, R. The Askey-Scheme of Hypergeometric Orthogonal Polynomials and Its q-Analogues, Delft University of Technology, Delft, Pays-Bas, 1998

[16] Mouayn, Z. Coherent state transforms attached to generalized Bargmann spaces on the complex plane, Math. Nachr., Volume 284 (2011) no. 14–15, pp. 1948-1954

[17] Odake, S.; Sasaki, R. q-oscillator from the q-Hermite polynomial, Phys. Lett. B, Volume 663 (2008), pp. 141-145

[18] Samuel Moreno, G.; García-Caballero Esther, M. Non-standard orthogonality for the little q-Laguerre polynomials, Appl. Math. Lett., Volume 22 (2009), pp. 1745-1749

[19] H.M. Srivastava, A.K. Agarwal, Generating functions for a class of q-polynomials, DM-426-IR, septembre 1986.

[20] Twareq Ali, S.; Antoine, J.-P.; Gazeau, J.-P. Coherent States, Wavelets and Their Generalizations, Springer Science+Business Media, New York, 2014

[21] Vasilevski, N.L. Poly-Fock spaces, differential operators and related topics, Oper. Theory, Adv. Appl., Volume 117 (2000), pp. 371-386

Cited by Sources: