Complex Hermite functions as Fourier–Wigner transform

DOI10.1080/10652469.2015.1095742zbMath1347.33018arXiv1506.07084OpenAlexW1943430943MaRDI QIDQ2790235

A. El Hamyani, Fatima Agorram, Arij Benkhadra, Allal Ghanmi

Publication date: 3 March 2016

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.07084

zbMATH Keywords

generating functionsHermite-Gauss functionscomplex Hermite polynomialsFourier-Wigner transform

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38)

Related Items (8)

Bivariate poly-analytic Hermite polynomials ⋮ Solving the heat equation for a perturbed magnetic Laplacian on the complex plane ⋮ Kernel representation formula: from complex to real Wiener-Itô integrals and vice versa ⋮ A special orthogonal complement basis for holomorphic-Hermite functions and associated 1d- and 2d-fractional Fourier transforms ⋮ On bicomplex Fourier–Wigner transforms ⋮ Constants of motion of the harmonic oscillator ⋮ Non-trivial 1d and 2d Segal–Bargmann transforms ⋮ On a novel class of polyanalytic Hermite polynomials

Cites Work

• Spectral properties of the Cauchy transform on \(L_2(\mathbb C,e^{-|z|^2}\lambda(z))\)
• Eigenvalue problems for the Schrödinger operator with the magnetic field on a compact Riemann manifold
• Spectral analysis of Schrödinger operators with magnetic fields
• A class of generalized complex Hermite polynomials
• Operational formulae for the complex Hermite polynomialsH_p,q(z, z¯)
• Asymptotic of complex hyperbolic geometry and L2-spectral analysis of Landau-like Hamiltonians
• Modular structures on trace class operators and applications to Landau levels
• Complex Hermite polynomials: Their combinatorics and integral operators
• Orthogonal Polynomials for Complex Gaussian Processes
• Orthogonal Polynomials of Several Variables

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