Positive convolution structure for a class of Heckman-Opdam hypergeometric functions of type BC

Details Positive convolution structure for a class of Heckman-Opdam hypergeometric functions of type BC Positive convolution structure for a class of Heckman-Opdam hypergeometric functions of type BC

2009-07-14

arxiv.org/abs/0907.2447v2

J. Funct. Anal. 258 (2010), 2779-2800

Mathematics

Representation Theory

Scientific paper

In this paper, we derive explicit product formulas and positive convolution structures for three continuous classes of Heckman-Opdam hypergeometric functions of type $BC$. For specific discrete series of multiplicities these hypergeometric functions occur as the spherical functions of non-compact Grassmann manifolds $G/K$ over one of the (skew) fields $\mathbb F= \mathbb R, \mathbb C, \mathbb H.$ We write the product formula of these spherical functions in an explicit form which allows analytic continuation with respect to the parameters. In each of the three cases, we obtain a series of hypergroup algebras which include the commutative convolution algebras of $K$-biinvariant functions on $G$.

Affiliated with

Also associated with

No associations

Rating

Positive convolution structure for a class of Heckman-Opdam hypergeometric functions of type BC does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Positive convolution structure for a class of Heckman-Opdam hypergeometric functions of type BC, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Positive convolution structure for a class of Heckman-Opdam hypergeometric functions of type BC will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-363564