Based on the theory of Dunkl operators, this paper presents a general concept of multivariable Hermite polynomials and Hermite functions which are associated with finite reflection groups on R . The definition and properties of these generalized Hermite systems extend naturally those of their classical counterparts; partial derivatives and the usual exponential kernel are here replaced by Dunkl...

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...

In this paper, we investigate the well-posedness for Cauchy problem multi-term time-fractional heat equation associated with Dunkl operator. The under consideration includes a linear combination of Caputo derivatives in time decreasing orders (0, 1) and positive constant coefficients one-dimensional operator.  To show solvability problem  use several important properties multinomial M...

Let G (α,β) λ be the eigenfunctions of the Dunkl–Cherednik operator T on R. In this paper we express the product G (α,β) λ (x)G (α,β) λ (y) as an integral in terms of G (α,β) λ (z) with an explicit kernel. In general this kernel is not positive. Furthermore, by taking the so–called rational limit, we recover the product formula of M. Rösler for the Dunkl kernel. We then define and study a convo...

We investigate algebraic structure for the BN -type Calogero model by using the exchange-operator formalism. We show that the set of the Jack polynomials whose arguments are Dunkl-type operators provides an orthogonal basis.

We investigate algebraic structure for the BN -type Calogero model by using the exchange-operator formalism. We show that the set of the Jack polynomials whose arguments are Dunkl-type operators provides an orthogonal basis.