Gelfand transforms of SO(3)-invariant Schwartz functions on the free group N_{3,2}
| dc.creator | Fischer, Veronique | |
| dc.creator | Ricci, Fulvio | |
| dc.date | 2008-09-11 | |
| dc.date.accessioned | 2026-07-07T10:02:14Z | |
| dc.date.available | 2026-07-07T10:02:14Z | |
| dc.description | The spectrum of a Gelfand pair $(K\ltimes N, K)$, where $N$ is a nilpotent group, can be embedded in a Euclidean space. We prove that in general, the Schwartz functions on the spectrum are the Gelfand transforms of Schwartz $K$-invariant functions on $N$. We also show the converse in the case of the Gelfand pair $(SO(3)\ltimes N_{3,2}, SO(3))$, where $N_{3,2}$ is the free two-step nilpotent Lie group with three generators. This extends recent results for the Heisenberg group. | |
| dc.description | 28 pages | |
| dc.identifier | https://arxiv.org/abs/0809.1952 | |
| dc.identifier | http://arxiv.org/abs/0809.1952 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/168899 | |
| dc.subject | Functional Analysis | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 43A80; 22E25 | |
| dc.title | Gelfand transforms of SO(3)-invariant Schwartz functions on the free group N_{3,2} | |
| dc.type | text |