The pluricomplex Poisson kernel for strongly convex domains
| dc.creator | Bracci, Filippo | |
| dc.creator | Patrizio, Giorgio | |
| dc.creator | Trapani, Stefano | |
| dc.date | 2005-07-12 | |
| dc.date | 2005-07-12 | |
| dc.date.accessioned | 2026-07-07T05:21:38Z | |
| dc.date.available | 2026-07-07T05:21:38Z | |
| dc.description | Let $D$ be a bounded strongly convex domain in the complex space of dimension $n$. Fixed a point $p\in \partial D$, we consider the solution of a homogeneous complex Monge-Ampere equation with simple pole at $p$. We prove that such a solution enjoys many properties of the classical Poisson kernel in the unit disc and thus deserves to be called the pluricomplex Poisson kernel of $D$ with pole at $p$. In particular we discuss extremality properties (such as a generalization of the classical Phragmen-Lindelof theorem), relations with the pluricomplex Green function of $D$, uniqueness in terms of the associated foliation and boundary behaviors and reproducing formulas for plurisubharmonic functions. | |
| dc.description | 31 pages | |
| dc.identifier | https://arxiv.org/abs/math/0507247 | |
| dc.identifier | http://arxiv.org/abs/math/0507247 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75760 | |
| dc.subject | Complex Variables | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 32W20; 32U35 | |
| dc.title | The pluricomplex Poisson kernel for strongly convex domains | |
| dc.type | text |