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...

Harmonic polynomials of type A are polynomials annihilated by the Dunkl Laplacian associated to the symmetric group acting as a reflection group on RN . The Dunkl operators are denoted by Tj for 1 ≤ j ≤ N, and the Laplacian ∆κ = ∑j=1 T2 j . This paper finds the homogeneous harmonic polynomials annihilated by all Tj for j > 2. The structure constants with respect to the Gaussian and sphere inner...

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 ...

On $$\mathbb {R}^N$$ equipped with a normalized root system R and multiplicity function $$k\ge 0$$ let us consider (not necessarily radial) kernel $$K({\mathbf {x}})$$ satisfying $$|\partial ^\beta K({\mathbf {x}})|\lesssim \Vert {\mathbf {x}}\Vert ^{-{\mathbf {N}}-|\beta |}$$ for $$|\beta |\le s$$ , where $${\mathbf {N}}$$ is the homogeneous dimension of $$({\mathbb {R}}^N,R,k)$$ . We addition...

the aim of this paper is to prove new quantitative uncertainty principle for the generalized fourier transform connected with a dunkl type operator on the real line. more precisely we prove an lp-lq-version of morgan's theorem.

We generate solvable cases of the two angular equations resulting from variable separation in three-dimensional Dunkl-Schrödinger equation expressed spherical coordinates. It is shown that Dunkl formalism interrelates these with trigonometric Pöschl-Teller systems. Based on this interrelation, we use point transformations and Darboux-Crum to construct new equations. Instead stationary energy, c...