The Choquet-Deny equation in a Banach space
| dc.creator | Jaworski, W. | |
| dc.creator | Neufang, M. | |
| dc.date | 2006-09-01 | |
| dc.date.accessioned | 2026-07-07T07:24:25Z | |
| dc.date.available | 2026-07-07T07:24:25Z | |
| dc.description | Let $G$ be a locally compact group and $π$ a representation of $G$ by weakly^* continuous isometries acting in a dual Banach space $E$. Given a probability measure $μ$ on $G$ we study the Choquet-Deny equation $π(μ)x=x$, $x\in E$. We prove that the solutions of this equation form the range of a projection of norm 1 and can be represented by means of a ``Poisson formula'' on the same boundary space that is used to represent the bounded harmonic functions of the random walk of law $μ$. The relation between the space of solutions of the Choquet-Deny equation in $E$ and the space of bounded harmonic functions can be understood in terms of a construction resembling the $W^*$-crossed product and coinciding precisely with the crossed product in the special case of the Choquet-Deny equation in the space $E=B(L^2(G))$ of bounded linear operators on $L^2(G)$. Other general properties of the Choquet-Deny equation in a Banach space are also discussed. | |
| dc.description | 30 pages | |
| dc.identifier | https://arxiv.org/abs/math/0609035 | |
| dc.identifier | http://arxiv.org/abs/math/0609035 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/116345 | |
| dc.subject | Functional Analysis | |
| dc.subject | Probability | |
| dc.subject | 22D12; 22D20; 43A05; 60B15; 60J50 | |
| dc.title | The Choquet-Deny equation in a Banach space | |
| dc.type | text |