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OPDAM FUNCTIONS: PRODUCT FORMULA AND CONVOLUTION STRUCTURE IN DIMENSION 1
 

Summary: OPDAM FUNCTIONS: PRODUCT FORMULA AND
CONVOLUTION STRUCTURE IN DIMENSION 1
J.-PH. ANKER, F. AYADI AND M. SIFI
Abstract. Let G
(,)
(x) be the eigenfunctions of the Dunkl-Cherednik oper-
ator T (,)
on R, with -1
2 . In this paper we express the product
G
(,)
(x)G
(,)
(y) as an integral in terms of G
(,)
(z) with an explicit kernel.
In general this kernel is not positive. Furthermore, by taking the so-called ratio-
nal limit, we recover the product formula for the Dunkl kernels proved in [13].
We then define and study a convolution structure associated to G
(,)

  

Source: Anker, Jean-Philippe - Laboratoire de Mathématiques et Applications, Physique Mathématique, Université d'Orléans

 

Collections: Mathematics