A positive radial product formula for the Dunkl kernel
| dc.creator | Rösler, Margit | |
| dc.date | 2002-10-09 | |
| dc.date.accessioned | 2026-07-07T04:51:46Z | |
| dc.date.available | 2026-07-07T04:51:46Z | |
| dc.description | It is an open conjecture that generalized Bessel functions associated with root systems have a positive product formula for non-negative multiplicity parameters of the associated Dunkl operators. In this paper, a partial result towards this conjecture is proven, namely a positive radial product formula for the non-symmetric counterpart of the generalized Bessel function, the Dunkl kernel. Radial hereby means that one of the factors in the product formula is replaced by its mean over a sphere. The key to this product formula is a positivity result for the Dunkl-type spherical mean operator. It can also be interpreted in the sense that the Dunkl-type generalized translation of radial functions is positivity-preserving. As an application, we construct Dunkl-type homogeneous Markov processes associated with radial probability distributions. | |
| dc.description | 25 pages | |
| dc.identifier | https://arxiv.org/abs/math/0210137 | |
| dc.identifier | http://arxiv.org/abs/math/0210137 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65230 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Representation Theory | |
| dc.subject | 33C52 (Primary); 44A35, 35L15 (Secondary) | |
| dc.title | A positive radial product formula for the Dunkl kernel | |
| dc.type | text |