In this paper we prove the absolute continuity of the representing measures of the Dunkl intertwining operator and of its dual. Next we present some applications of this result. Key word : Dunkl intertwining operator and its dual. Absolute continuity of the representing measures. MSC (2000) : 33C80, 51F15, 44A15. Introduction We consider the differential-difference operators on R introduced by ...

Abstract In this paper we investigate certain integral operator involving Jacobi–Dunkl functions in a class of generalized functions. We utilize convolution products, approximating identities, and several axioms to allocate the desired spaces The existing theory (Ben Salem Ahmed Ramanujan J. 12(3):359–378, 2006) is extended applied new addressed set Boehmians. Various embeddings characteristics...

A q-analogue of the type A Dunkl operator and integral kernel We introduce the q-analogue of the type A Dunkl operators, which are a set of degree–lowering operators on the space of polynomials in n variables. This allows the construction of raising/lowering operators with a simple action on non-symmetric Macdonald polynomials. A bilinear series of non-symmetric Macdonald polynomials is introdu...

This paper studies the asymptotic behavior of the integral kernel of the Dunkl transform, the so-called Dunkl kernel, when one of its arguments is fixed and the other tends to infinity either within a Weyl chamber of the associated reflection group, or within a suitable complex domain. The obtained results are based on the asymptotic analysis of an associated system of ordinary differential equ...

In this paper, we introduce a new differential-difference operator Tξ (ξ ∈ R ) by using projections associated to orthogonal subsystems in root systems. Similarly to Dunkl theory, we show that these operators commute and we construct an intertwining operator between Tξ and the directional derivative ∂ξ. In the case of one variable, we prove that the Kummer functions are eigenfunctions of this o...

Based on a result of Rösler and Voit for ultraspherical polynomials, we derive an uncertainty principle for compact Riemannian manifolds M . The frequency variance of a function in L(M) is therein defined by means of the radial part of the Laplace-Beltrami operator. The proof of the uncertainty rests upon Dunkl theory. In particular, a special differential-difference operator is constructed whi...

For a better understanding of the physical systems, even at quantum level, thermal quantities can be investigated. Recently, we realized that parity system also examined simultaneously, by substituting Dunkl operator with ordinary differential in mechanics. In this manuscript, consider two relativistic Dunkl-oscillators and investigate their well-known statistical methods. Besides, establish re...