arXiv subjects

Khalil Lamsaf

Publications and source records attributed to Khalil Lamsaf.

2 recordsLinked to original sources

arXiv2021

Two-dimensional $(p,q)$-heat polynomials of Gould--Hopper type

We introduce a new class of holomorphic polynomials extending the classical Gould--Hopper to two complex variables. The considered polynomials include the $1$-D and $2$-D holomorphic and polyanalytic Itô--Hermite polynomials as particular cases. We emphasize studying their operational representation, various generating functions, and recurrence relations. We also establish some special identities including multiplication and addition formulas of Runge type, as well as the Nielson type formulas. Higher-order partial differential equations are analyzed and the connection to Gould-Hopper polynomials and hypergeometric functions are investigated.

math.CA↗

arXiv2019

Bivariate poly-analytic Hermite polynomials

A new class of bivariate poly-analytic Hermite polynomials is considered. We show that they are realizable as the Fourier-Wigner transform of the univariate complex Hermite functions and form a nontrivial orthogonal basis of the classical Hilbert space on the two-complex space with respect to the Gaussian measure. Their basic properties are discussed, such as their three term recurrence relations, operational realizations and differential equations (Bochner's property) they obey. Different generating functions of exponential type are obtained. Integral and exponential operational representations are also derived. Some applications in the context of integral transforms and the concrete spectral theory of specific magnetic Laplacians are discussed.

math.CV↗