On uniform asymptotic upper density in locally compact abelian groups
| dc.creator | Revesz, Szilard Gy. | |
| dc.date | 2009-04-09 | |
| dc.date.accessioned | 2026-07-07T13:02:00Z | |
| dc.date.available | 2026-07-07T13:02:00Z | |
| dc.description | Starting out from results known for the most classical cases of N, Z^d, R^d or for sigma-finite abelian groups, here we define the notion of asymptotic uniform upper density in general locally compact abelian groups. Even if a bit surprising, the new notion proves to be the right extension of the classical cases of Z^d, R^d. The new notion is used to extend some analogous results previously obtained only for classical cases or sigma-finite abelian groups. In particular, we show the following extension of a well-known result for Z of Furstenberg: if in a general locally compact Abelian group G a subset S of G has positive uniform asymptotic upper density, then S-S is syndetic. | |
| dc.identifier | https://arxiv.org/abs/0904.1567 | |
| dc.identifier | http://arxiv.org/abs/0904.1567 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/226341 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Group Theory | |
| dc.subject | 22B05 | |
| dc.title | On uniform asymptotic upper density in locally compact abelian groups | |
| dc.type | text |