Positivity of Dunkl's intertwining operator
| dc.creator | Rösler, Margit | |
| dc.date | 1997-10-24 | |
| dc.date | 1997-12-11 | |
| dc.date.accessioned | 2026-07-07T05:57:39Z | |
| dc.date.available | 2026-07-07T05:57:39Z | |
| dc.description | For a finite reflection group on $\b R^N,$ the associated Dunkl operators are parametrized first-order differential-difference operators which generalize the usual partial derivatives. They generate a commutative algebra which is - under weak assumptions - intertwined with the algebra of partial differential operators by a unique linear and homogeneous isomorphism on polynomials. In this paper it is shown that for non-negative parameter values, this intertwining operator is positivity-preserving on polynomials and allows a positive integral representation on certain algebras of analytic functions. This result in particular implies that the generalized exponential kernel of the Dunkl transform is positive-definite. | |
| dc.description | 18 pages, LaTeX2e; some minor corrections made | |
| dc.identifier | https://arxiv.org/abs/q-alg/9710029 | |
| dc.identifier | http://arxiv.org/abs/q-alg/9710029 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/88064 | |
| dc.subject | Quantum Algebra | |
| dc.subject | 33C80 (Primary) 44A15, 33C50 (Secondary) | |
| dc.title | Positivity of Dunkl's intertwining operator | |
| dc.type | text |