Positivity of Dunkl's intertwining operator via the trigonometric setting

Details Positivity of Dunkl's intertwining operator via the trigonometric setting Positivity of Dunkl's intertwining operator via the trigonometric setting

2004-05-19

arxiv.org/abs/math/0405368v2

Mathematics

Classical Analysis and ODEs

9 pages; revised and slightly extended version. To appear in Int.Math.Res.Not

Scientific paper

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.

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