A generalized spin Sutherland model including a three-body potential is proposed. The problem is analyzed in terms of three first-order differential-difference operators, obtained by combining SUSYQM supercharges with the elements of the dihedral group D6. Three alternative commuting operators are also introduced. PACS: 03.65.Fd, 02.20.Df, 11.30.Pb Directeur de recherches FNRS; E-mail: cquesne@...

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 ...

Graphene-based materials are thought to revolutionize entire industries. Therefore, many research being carried on graphene theoretically and experimentally. On the other hand, recent studies show that use of Dunkl derivative, instead ordinary allows concept parity be interpreted together with physical quantities. In this manuscript, we investigate thermal quantities under constant magnetic fie...

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+).  

Vector-valued Jack polynomials associated to the symmetric group SN are polynomials with multiplicities in an irreducible module of SN and which are simultaneous eigenfunctions of the Cherednik–Dunkl operators with some additional properties concerning the leading monomial. These polynomials were introduced by Griffeth in the general setting of the complex reflections groups G(r, p,N) and studi...

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...

The one-dimensional Dunkl operator Dk with a non-negative parameter k, is considered under an arbitrary nonlocal boundary value condition. The right inverse operator of Dk, satisfying this condition is studied. An operational calculus of Mikusiński type is developed. In the frames of this operational calculi an extension of the Heaviside algorithm for solution of nonlocal Cauchy boundary value ...