References
- Agorram A, Benkhadra A, El Hamyani A, et al. Complex Hermite functions as Fourier-Wigner transform. Integral Transforms Spec Funct. 2016;27(2):94–100. doi: 10.1080/10652469.2015.1095742
- El Fardi A, Ghanmi A, Imlal L, et al. Analytic and arithmetic properties of the (Γ,χ)-automorphic reproducing kernel function and associated Hermite-Gauss series. Ramanujan J. 2019;48(1):47–62. doi: 10.1007/s11139-018-0032-9
- Ghanmi A. A class of generalized complex Hermite polynomials. J Math Anal Appl. 2008;340:1395–1406. doi: 10.1016/j.jmaa.2007.10.001
- Ghanmi A. Mehler's formulas for the univariate complex Hermite polynomials and applications. Math Methods Appl Sci Math Methods Appl Sci. 2017;40(18):7540–7545. doi: 10.1002/mma.4545
- Intissar A, Intissar A. Spectral properties of the Cauchy transform on L2(C;e−∣z∣2dλ). J Math Anal Appl. 2006;313(2):400–418. doi: 10.1016/j.jmaa.2005.09.056
- Ismail MEH. Analytic properties of complex Hermite polynomials. Trans Amer Math Soc. 2016;368(2):1189–1210. doi: 10.1090/tran/6358
- Zayed A. Two-dimensional fractional Fourier transform and some of its properties. Integral Transforms Spec Funct. 2018;29(7):553–570. doi: 10.1080/10652469.2018.1471689
- Bargmann V. On a Hilbert space of analytic functions and an associated integral transform. Comm Pure Appl Math. 1961;14:187–214. doi: 10.1002/cpa.3160140303
- Segal I. Mathematical characterization of the physical vacuum for a linear Bose-Einstein field. Illinois J Math. 1962;6:500–523.
- Folland GB. Harmonic analysis in phase space. Annals of Mathematics Studies, 122. Princeton (NJ): Princeton University Press; 1989.
- Neretin YA. Lectures on Gaussian integral operators and classical groups. EMS Series of Lectures in Mathematics. Zürich: European Mathematical Society (EMS); 2011.
- Gross L, Malliavin P. Hall's transform and the Segal–Bargmann map. In: Ikeda N, et al., editors. Itô's stochastic calculus and probability. Berlin: Springer; 1996. p. 78–116.
- Hall BC. The Segal–Bargmann ‘coherent-state’ transform for Lie groups. J Funct Anal. 1994;122:103–151. doi: 10.1006/jfan.1994.1064
- Mourao J, Nunes JP, Qian T. Coherent state transforms and the Weyl equation in Clifford analysis. J Math Phys. 2017;58(1):013503, 12. doi: 10.1063/1.4974449
- Mouayn Z. Coherent state transforms attached to generalized Bargmann spaces on the complex plane. Math Nachr. 2011;284(14–15):1948–1954. doi: 10.1002/mana.200910191
- Vasilevski NL. Poly-Fock spaces. Oper Theory Adv App. 2000;117:371–386.
- Wünsche A. Laguerre 2D-functions and their application in quantum optics. J Phys A. 1998;31(40):8267–8287. doi: 10.1088/0305-4470/31/40/017
- Ghanmi A. Operational formulae for the complex Hermite polynomials Hp,q(z,z¯). Integral Transforms Spec Funct. 2013;24(11):884–895. doi: 10.1080/10652469.2013.772172
- Abreu LD. Sampling and interpolation in Bargmann–Fock spaces of polyanalytic functions. Appl Comput Harmon Anal. 2010;29(3):287–302. doi: 10.1016/j.acha.2009.11.004
- Ghanmi A, Intissar A. Asymptotic of complex hyperbolic geometry and L2-spectral analysis of Landau-like Hamiltonians. J Math Phys. 2005;46(3):032107. doi: 10.1063/1.1853505
- Rainville ED. Special functions. Bronx (NY): Chelsea Publishing Co.; 1960.
- Pool JCT. Mathematical aspect of Weyl correspondence. J Math Phys. 1966;7:66–76. doi: 10.1063/1.1704817
- Thangavelu S. Harmonic analysis on the Heisenberg group. Progress in Mathematics, 159. Boston (MA): Birkhäuser Boston, Inc.; 1998.
- Shun-Long L. On the Bargmann transform and the wigner transform. Bull London Math Soc. 1998;30:413–418. doi: 10.1112/S0024609398004457
- Gazeau J-P. Coherent states in quantum physics. Berlin: Wiley-VCH; 2009.