On the estimates of Dunkl kernels (Q2036586)

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. In particular the authors give upper bounds for \(E_k (x, gy)\) and \(\vert E_k(ix,gy)\vert \).