In this paper, we study some important basic properties of Dunkl-bounded variation functions. particular, derive a way approximating functions by smooth and establish version the Gauss–Green Theorem. We also Dunkl BV capacity investigate measure theoretic properties, moreover, show that Hausdorff codimension one have same null sets. Finally, develop characterization heat semigroup space, thereb...

A singular polynomial is one which is annihilated by all Dunkl operators for a certain parameter value. These polynomials were first studied by Dunkl, de Jeu and Opdam, (Trans. Amer. Math. Soc. 346 (1994), 237-256). This paper constructs a family of such polynomials associated to the irreducible representation (N − 2, 1, 1) of the symmetric group SN for odd N and parameter values − 1 2 ,− 3 2 ,...

Abstract. We provide two equivalent approaches for computing the tail distribution of the first hitting time of the boundary of the Weyl chamber by a radial Dunkl process. The first approach is based on a spectral problem with initial value. The second one expresses the tail distribution by means of the W -invariant Dunkl–Hermite polynomials. Illustrative examples are given by the irreducible r...

In this paper, we will give some results on the support of Dunkl translations compactly supported functions. Then define Dunkl-type $BMO$ space and Riesz transforms for transform $L^\infty$, prove boundedness from $L^\infty$ to under uniform assumption translations. The proof definition in setting be harder than classical case lack similar properties that We also extend preciseness description ...

In this paper, we consider the normalized Bessel function of index ?>?12, find an integral representation term xnj?+n(x)j?(y). This allows us to establish a product formula for generalized Hankel B??,n on R. is kernel transform F?,n arising from Dunkl theory. Indeed show that B??,n(x)B??,n(y) can be expressed as in terms B??,n(z) with explicit invoking Gegenbauer polynomials all n?N?. The obtai...