The p-harmonic boundary for finitely generated groups and the first reduced \ell_p-cohomology
| dc.creator | Puls, Michael | |
| dc.date | 2007-09-19 | |
| dc.date | 2008-04-03 | |
| dc.date.accessioned | 2026-07-07T09:29:47Z | |
| dc.date.available | 2026-07-07T09:29:47Z | |
| dc.description | Let $p$ be a real number greater than one and let $G$ be a finitely generated, infinite group. In this paper we introduce the $p$-harmonic boundary of $G$. We then characterize the vanishing of the first reduced $\ell^p$-cohomology of $G$ in terms of the cardinality of this boundary. Some properties of $p$-harmonic boundaries that are preserved under rough isometries are also given. We also study the relationship between translation invariant linear functionals on a certain difference space of functions on $G$, the $p$-harmonic boundary of $G$ and the first reduced $\ell^p$-cohomology of $G$. | |
| dc.description | In the original paper the integers provide a counter example to Proposition 3.3. The reason is that I gave an incorrect definition for $p$-harmonic boundary. The new version has the correct defintion and some smaller changes | |
| dc.identifier | https://arxiv.org/abs/0709.2941 | |
| dc.identifier | http://arxiv.org/abs/0709.2941 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/157912 | |
| dc.subject | Functional Analysis | |
| dc.subject | Group Theory | |
| dc.subject | 43A15, 20F65, 31C20, 60J50 | |
| dc.title | The p-harmonic boundary for finitely generated groups and the first reduced \ell_p-cohomology | |
| dc.type | text |