The operator that intertwines between the $\mathbb{Z}_2$ - Dunkl and derivative is shown to have a realization in terms of oscillator operators one dimension. This observation rests on fact intertwining maps Hermite polynomials generalized polynomials.

For a finite reflection group on R , the associated Dunkl operators are parametrized firstorder differential-difference operators which generalize the usual partial derivatives. They generate a commutative algebra which is – under weak assumptions – intertwined with the algebra of partial differential operators by a unique linear and homogeneous isomorphism on polynomials. In this paper it is s...

Using a generalized translation operator, we obtain a generalization of Theorem 5 in [4] for the Bessel transform for functions satisfying the (delta;gamma ; 2)-BesselLipschitz condition in L_{2;alpha}(R+).  

In this paper, we define subspaces of L by differences using the Dunkl translation operators that we call Besov-Dunkl spaces. We provide characterization of these spaces by the Dunkl convolution.

In this paper, we consider the normalized Bessel function of index ?>?12, find an integral representation term xnj?+n(x)j?(y). This allows us to establish a product formula for generalized Hankel B??,n on R. is kernel transform F?,n arising from Dunkl theory. Indeed show that B??,n(x)B??,n(y) can be expressed as in terms B??,n(z) with explicit invoking Gegenbauer polynomials all n?N?. The obtai...

In 1961, Bargmann introduced the classical Fock space $$\mathscr {F}(\mathbb {C}^{d})$$ and in 1984, Cholewinsky generalized {F}_{\alpha ,e}(\mathbb . These two spaces are aim of many works, have applications mathematics, physics, quantum mechanics. this work, we introduce study }(\mathbb associated to Dunkl operators $$T_{\alpha _{j}}$$ with $$\alpha _{j}>-1/2$$ for all $$j=1,\ldots ,d$$ This ...

The classical theory of Hardy spaces on n has received an important impetus from the work of Fefferman and Stein, Lu and Yang 1, 2 . Their work resulted in many applications involving sharp estimates for convolution and multiplier operators. By using the technique of Herz-type Hardy spaces for the Dunkl operator Λα, we are attempting in this paper to study the Dunkl convolution operators, andwe...

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 explicit relation connecting them with the generalized Laguerre polynomials. A link is established with the generalized Hermite polynomials related ...