Polynomially growing pluriharmonic functions on Siegel domains
Volume 109 / 2007
Colloquium Mathematicum 109 (2007), 31-60
MSC: 32M10, 32M15, 43A65, 43A80, 22E27.
DOI: 10.4064/cm109-1-4
Abstract
Let $\cal{D}$ be a symmetric type two Siegel domain over the cone of positive definite Hermitian matrices and let $\mathbf{N}({\mit\Phi} )\mathbf{S}$ be a solvable Lie group acting simply transitively on $\mathcal{D}$. We characterize polynomially growing pluriharmonic functions on $\mathcal{D}$ by means of three $\mathbf{N}({\mit\Phi} )\mathbf{S}$-invariant second order elliptic degenerate operators.
