On Mixing and Ergodicity in Locally Compact Motion Groups
| dc.creator | Anoussis, M. | |
| dc.creator | Gatzouras, D. | |
| dc.date | 2006-12-10 | |
| dc.date.accessioned | 2026-07-07T12:07:21Z | |
| dc.date.available | 2026-07-07T12:07:21Z | |
| dc.description | Let $G$ be a semi-direct product $G=A\times_ϕK$ with $A$ Abelian and $K$ compact. We characterize spread-out probability measures on $G$ that are mixing by convolutions by means of their Fourier transforms. A key tool is a spectral radius formula for the Fourier transform of a regular Borel measure on $G$ that we develop, and which is analogous to the well-known Beurling--Gelfand spectral radius formula. For spread-out probability measures on $G$, we also characterize ergodicity by means of the Fourier transform of the measure. Finally, we show that spread-out probability measures on such groups are mixing if and only if they are weakly mixing. | |
| dc.identifier | https://arxiv.org/abs/math/0612262 | |
| dc.identifier | http://arxiv.org/abs/math/0612262 | |
| dc.identifier | Journal fuer die reine und angewandte Mathematik, 625 (2008), 1--28. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/208938 | |
| dc.subject | Functional Analysis | |
| dc.subject | Probability | |
| dc.title | On Mixing and Ergodicity in Locally Compact Motion Groups | |
| dc.type | text |