A+ CATEGORY SCIENTIFIC UNIT

Polynomially growing pluriharmonic functions on Siegel domains

Volume 109 / 2007

Monika Gilżyńska 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.

Authors

  • Monika GilżyńskaZaciszna 7/16
    55-200 Oława, Poland
    e-mail

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