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...

Some estimates are proved for the generalized Fourier-Bessel transform in the space (L^2) (alpha,n)-index certain classes of functions characterized by the generalized continuity modulus.

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.