Results 71 to 80 of about 1,609 (94)

Oppenheim's problem and related inequalities for Dunkl kernels [PDF]

Mathematical Inequalities & Applications, 2014
openaire   +1 more source

Asymptotic Analysis for the Dunkl Kernel

Journal of Approximation Theory, 2002
This paper studies the asymptotic behavior of the integral kernel of the Dunkl transform, the so-called Dunkl kernel, when one of its arguments is fixed and the other tends to infinity either within a Weyl chamber of the associated reflection group, or within a suitable complex domain.
Margit Rösler, Marcel de Jeu
exaly   +6 more sources

Explicit formulas for the Dunkl dihedral kernel and the (κ,a)-generalized Fourier kernel [PDF]

Journal of Mathematical Analysis and Applications, 2018
In this paper, a new method is developed to obtain explicit and integral expressions for the kernel of the $(κ, a)$-generalized Fourier transform for $κ=0$. In the case of dihedral groups, this method is also applied to the Dunkl kernel as well as the Dunkl Bessel function.
Denis Constales, Hendrik De Bie, Pan Lian   +2 more
exaly   +5 more sources

On the Estimates of Dunkl Kernels

Analysis Mathematica, 2021
The authors study properties of the Dunkl operator \(D_\xi(k)\) on \(\mathbb{R}^n\). They investigate the asymptotic behavior of the Dunkl kernel \(E_k(x,y)\) and give estimates for the Dunkl kernel which is uniform in each convex cone contained in an open Weyl chamber.
Amri, B., Gasmi, A.
openaire   +2 more sources

An integral expression for the Dunkl kernel in the dihedral setting [PDF]

Journal of Applied Analysis, 2017
Abstract Using the results in [12] where a construction of the Dunkl intertwining operator for a large set of regular parameter functions is provided, we establish an integral expression for the Dunkl kernel in the context of the dihedral group
M Maslouhi
exaly   +4 more sources

Fock Spaces for the q-Dunkl Kernel

Advances in Pure Mathematics, 2012
In this work, we introduce a class of Hilbert spaces of entire functions on the disk , 0＜q＜1 , with reproducing kernel given by the q-Dunkl kernel . The definition and properties of the space extend naturally those of the well-known classical Fock space.
Fethi Soltani
exaly   +3 more sources

An estimate for the Dunkl kernels of type $$B_2 $$

Bollettino dell'Unione Matematica Italiana, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Amri, Béchir, Bedhiafi, Mounir
openaire   +2 more sources

Spectral decomposition of Dunkl Laplacian and application to a radial integral representation for the Dunkl kernel

Journal of Pseudo-Differential Operators and Applications, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Askour, Nour Eddine, El Mourni, Abdelilah, El Yazidi, Imane   +2 more
exaly   +3 more sources

A Reduction Formula for the Dunkl Kernel for the Root Systems of Type A

Mediterranean Journal of Mathematics
In this paper, we provide a reduction formula for the Dunkl kernel for the root systems of type $A$. The Dunkl kernel for the root system $A_n$ is expressed as an integral involving the Dunkl kernel for the root system $A_{n-1}$. The corresponding reduction formula for the intertwining operator $V_k$ is given.
P Sawyer
exaly   +3 more sources