73 citations · 176 across the 40 of their papers we have counts for
10 papers · 1 filter
-complex Itô--Hermite polynomials
Abdelhadi Benahmadi, Allal Ghanmi
We introduce two classes of -Itô--Hermite polynomials, the post-quantum analogs of the -Itô--Hermite polynomials introduced recently by Ismail and Zhang. We study their b…
Two-dimensional -heat polynomials of Gould--Hopper type
Allal Ghanmi, Khalil Lamsaf
We introduce a new class of holomorphic polynomials extending the classical Gould--Hopper to two complex variables. The considered polynomials include the -D and -D holomorph…
The orthogonal complement of the Hilbert space associated to holomorphic Hermite polynomials
Abdelhadi Benahmadi, Allal Ghanmi, Mohammed Souid El Ainin
We study the orthogonal complement of the Hilbert subspace considered by by van Eijndhoven and Meyers in [J. Math. Anal. Appl. 146 (1990), no. 1, 89--98} and associated to holomorp…
Mehler's formulas for the univariate complex Hermite polynomials and applications
Allal Ghanmi
We give two widest Mehler's formulas for the univariate complex Hermite polynomials , by performing double summations involving the products $u^m H_{m,n}^ν(z,\overline{z…
Generalized Zernike polynomials: Integral representation and Cauchy transform
A. El Hamyani, A. Ghanmi, A. Intissar
The aim of this paper is two fold. We derive an integral representation for the generalized 2D Zernike polynomials which are of independent interest and give the explicit expressio…
Complex Hermite functions as Fourier-Wigner transform
Fatima Agorram, Arij Benkhadra, Amal El Hamyani +1
We prove that the complex Hermite polynomials H_{m,n} on the complex plane can be realized as the Fourier-Wigner transform of the well-known real Hermite…