The Dunkl transform is an integral transform on R" which generalises the classical Fourier transform. On suitable function spaces, it establishes a natural correspondence between the action of multiplication operators on one hand and so-called Dunkl operators on the other. These are differential-difference operators, generalising the usual partial derivatives, which are associated with a finite...

A new family of AN -type Dunkl operators preserving a polynomial subspace of finite dimension is constructed. Using a general quadratic combination of these operators and the usual Dunkl operators, several new families of exactly and quasi-exactly solvable quantum spin Calogero–Sutherland models are obtained. These include, in particular, three families of quasi-exactly solvable elliptic spin H...

In this paper, we introduce the notion of Dunkl-classical orthogonal polynomials. Then, we show that generalized Hermite and generalized Gegenbauer polynomials are the only Dunkl-classical symmetric orthogonal polynomials by solving a suitable differential-difference equation. 2006 Elsevier Inc. All rights reserved.

For certain negative rational numbers κ0, called singular values, and associated with the symmetric group SN on N objects, there exist homogeneous polynomials annihilated by each Dunkl operator when the parameter κ = κ0. It was shown by the author, de Jeu and Opdam (Trans. Amer. Math. Soc. 346 (1994), 237-256) that the singular values are exactly the values − n with 2 ≤ n ≤ N , m = 1, 2, . . . ...

The aim of this work is to introduce a novel concept, Riesz–Dunkl fractional derivatives, within the context Dunkl-type operators. A particularly noteworthy revelation that when specific parameter κ equals zero, derivative smoothly reduces both well-known Riesz and second-order derivative. Furthermore, we new concept: Sobolev space. This space defined characterized using versatile framework Dun...

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...