Results 31 to 40 of about 2,079 (108)

An Alternative Definition of the Hermite Polynomials Related to the Dunkl Laplacian [PDF]

, 2008
We introduce the so-called Clifford-Hermite polynomials in the framework of Dunkl operators, based on the theory of Clifford analysis. Several properties of these polynomials are obtained, such as a Rodrigues formula, a differential equation and an ...
De Bie, Hendrik
core   +8 more sources

(δ,γ)-Jacobi-Dunkl Lipschitz Functions in the Space L2(R,Aα,β(x)dx)

International Journal of Analysis and Applications, 2015
Using a generalized Jacobi-Dunkl translation, we obtain an analog of Theorem 5.2 in Younis paper [7] for the Jacobi-Dunkl transform for functions satisfying the (δ,γ)-Jacobi-Dunkl Lipschitz condition in the space L2(R,Aα,β(x)dx), α ≥ β ≥−1/2, α ≠−1/2.
R. Daher, S. El Ouadih
doaj   +2 more sources

Two Versions of Dunkl Linear Canonical Wavelet Transforms and Applications

Mathematics
Among the class of generalized Fourier transformations, the linear canonical transform is of crucial importance, mainly due to its higher degrees of freedom compared to the conventional Fourier and fractional Fourier transforms.
Saifallah Ghobber, Hatem Mejjaoli
doaj   +1 more source

Orthogonality of Hermite polynomials in superspace and Mehler type formulae [PDF]

, 2011
In this paper, Hermite polynomials related to quantum systems with orthogonal O(m)-symmetry, finite reflection group symmetry G < O(m), symplectic symmetry Sp(2n) and superspace symmetry O(m) x Sp(2n) are considered.
Coulembier, Kevin, De Bie, Hendrik, Sommen, Frank   +2 more
core   +3 more sources

Dunkl Hyperbolic Equations [PDF]

, 2008
We introduce and study the Dunkl symmetric systems. We prove the well-posedness results for the Cauchy problem for these systems. Eventually we describe the finite speed of it. Next the semi-linear Dunkl-wave equations are also studied.Comment: This is a
Mejjaoli, Hatem
core   +5 more sources

The class Bp for weighted generalized Fourier transform inequalities

Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica, 2015
In the present paper, we prove weighted inequalities for the Dunkl transform (which generalizes the Fourier transform) when the weights belong to the well-known class Bp.
Chokri Abdelkefi, Mongi Rachdi
doaj   +1 more source

Fractional Supersymmetric Hermite Polynomials

Mathematics, 2020
We provide a realization of fractional supersymmetry quantum mechanics of order r, where the Hamiltonian and the supercharges involve the fractional Dunkl transform as a Klein type operator.
Fethi Bouzeffour, Wissem Jedidi
doaj   +1 more source

On Harmonic Analysis Operators in Laguerre-Dunkl and Laguerre-Symmetrized Settings [PDF]

, 2016
We study several fundamental harmonic analysis operators in the multi-dimensional context of the Dunkl harmonic oscillator and the underlying group of reflections isomorphic to $\mathbb{Z}_2^d$.
Nowak, Adam, Stempak, Krzysztof, Szarek, Tomasz Z.   +2 more
core   +1 more source

Beurling’s Theorem for the Q-Fourier-Dunkl Transform

Kragujevac Journal of Mathematics, 2021
The Q-Fourier-Dunkl transform satisfies some uncertainty principles in a similar way to the Euclidean Fourier transform. By using the heat kernel associated to the Q-Fourier-Dunkl operator, we establish an analogue of Beurling’s theorem for the Q-Fourier-Dunkl transform ℱQ on ℝ.
Loualid, El Mehdi, Achak, Azzedine, Daher, Radouan   +2 more
openaire   +2 more sources

A Multiplier Theorem for Herz-Type Hardy Spaces Associated with the Dunkl Transform

Abstract and Applied Analysis, 2013
The main purpose of this paper is to establish a Hörmander multiplier theorem for Herz-type Hardy spaces associated with the Dunkl transform.
A. Gasmi
doaj   +1 more source