Positivity of Dunkl's intertwining operator via the trigonometric setting
arXiv:math/0405368
Abstract
In this note, a new proof for the positivity of Dunkl's intertwining operator in the crystallographic case is given. It is based on an asymptotic relationship between the Opdam-Cherednik kernel and the Dunkl kernel as recently observed by M. de Jeu, and on positivity results of S. Sahi for the Heckman-Opdam polynomials and their non-symmetric counterparts.
9 pages; revised and slightly extended version. To appear in Int.Math.Res.Not