6 papers
-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…
Dual of 2D fractional Fourier transform associated to Itô--Hermite polynomials
Abdelhadi Benahmadi, Allal Ghanmi
A class of integral transforms, on the planar Gaussian Hilbert space with range in the weighted Bergman space on the bi-disk, is defined as the dual transforms of the 2d fractional…
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…
On a novel class of polyanalytic Hermite polynomials
Abdelhadi Benahmadi, Allal Ghanmi
We carry out some algebraic and analytic properties of a new class of orthogonal polyanalytic polynomials, including their operational formulas, recurrence relations, generating fu…
Non-trivial 1d and 2d integral transforms of Segal-Bargmann type
Abdelhadi Benahmadi, Allal Ghanmi
Generating functions for the univariate complex Hermite polynomials (UCHP) are employed to introduce some non-trivial one and two-dimensional integral transforms of Segal-Bargmann…
On composition of Segal-Bargmann transforms
Abdelhadi Benahmadi, Kamal Diki, Allal Ghanmi
We introduce and discuss some basic properties of some integral transforms in the framework of specific functional Hilbert spaces, the holomorphic Bargmann-Fock spaces on $\mathbb{…