$q$-Analogue of the Dunkl transform on the real line
| dc.creator | Bettaibi, Néji | |
| dc.creator | bettaieb, Rym H. | |
| dc.date | 2007-12-29 | |
| dc.date.accessioned | 2026-07-07T08:51:53Z | |
| dc.date.available | 2026-07-07T08:51:53Z | |
| dc.description | In this paper, we consider a $q$-analogue of the Dunkl operator on $\mathbb{R}$, we define and study its associated Fourier transform which is a $q$-analogue of the Dunkl transform. In addition to several properties, we establish an inversion formula and prove a Plancherel theorem for this $q$-Dunkl transform. Next, we study the $q$-Dunkl intertwining operator and its dual via the $q$-analogues of the Riemann-Liouville and Weyl transforms. Using this dual intertwining operator, we provide a relation between the $q$-Dunkl transform and the $q^2$-analogue Fourier transform introduced and studied by R. Rubin. | |
| dc.description | 20 pages. to appear in Tamsui Oxford Journal Sciences | |
| dc.identifier | https://arxiv.org/abs/0801.0069 | |
| dc.identifier | http://arxiv.org/abs/0801.0069 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/145094 | |
| dc.subject | Quantum Algebra | |
| dc.subject | 33D15; 39A12 | |
| dc.title | $q$-Analogue of the Dunkl transform on the real line | |
| dc.type | text |