Journal of Lie Theory Vol. 12, No. 1, pp. 217243 (2002) 

Poisson kernels and pluriharmonic ${\cal H}^2$ functions on homogeneous Siegel domainsBartosz TrojanBartosz TrojanInstytut Matematyczny Uniwersytet Wroc\l awski Plac Grunwaldzki 2/4 50384 Wroc\l aw Poland trojan@math.uni.wroc.pl Abstract: In the paper we prove that a real function $F$ defined on a homogeneous not necessarily symmetric Siegel domain satisfying an ${cal H}^2$ condition is pluriharmonic if and only if ${\bf H} F=0$, ${\cal L}F=0$, $L F=0$, where ${\bf H}$, $\cal L$, $L$ are second order differential operators. This generalizes the result of Damek, Hulanicki, Müller, and Peloso [3] where symmetric domains were considered. Our approach to study nonsymmetric case is based on $T$algebras introduced by Vinberg [11]. Full text of the article:
Electronic fulltext finalized on: 30 Oct 2001. This page was last modified: 9 Nov 2001.
© 2001 Heldermann Verlag
