Journal of Lie Theory

no. 1
Poisson Kernels and Pluriharmonic H2 Functions on Homogeneous Siegel Domains
Journal of Lie Theory, Volume 12 (2002) no. 1, pp. 217-243
\newcommand{\hp}[1]{$\mathcal{H}^{#1}$} We prove that a real function $F$ defined on a homogeneous not necessarily symmetric Siegel domain satisfying an \hp{2} condition is pluriharmonic if and only if $\mathbf{H} F=0$, $\mathcal{L}F=0$, $L F=0$, where $\mathbf{H}$, $\mathcal{L}$, $L$ are second order differential operators. This generalizes the result of E. Damek, A. Hulanicki, D. M\"uller, and M. Peloso ["Pluriharmonic \hp{^2} functions on symmetric irreducible Siegel domains, Geom. Funct. Anal. 10 (2000) 1090--1117], where symmetric domains were considered. Our approach to study non-symmetric case is based on $T$-algebras introduced by E. B. Vinberg ["The theory of convex homogeneous cones, Trans. Moscow Math. Soc. 12 (1963) 340--403].
DOI: 10.5802/jolt.259
Classification: 31C10, 32M10, 43A85, 22E30
Keywords: \(T\)-algebra, Poisson integral, pluriharmonic functions, Siegel domains 
@article{JOLT_2002_12_1_a10,
     author = {B. Trojan},
     title = {Poisson {Kernels} and {Pluriharmonic} {H\protect\textsuperscript{2}} {Functions} on {Homogeneous} {Siegel} {Domains}},
     journal = {Journal of Lie Theory},
     pages = {217--243},
     year = {2002},
     volume = {12},
     number = {1},
     doi = {10.5802/jolt.259},
     zbl = {0997.31006},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.259/}
}
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B. Trojan. Poisson Kernels and Pluriharmonic H2 Functions on Homogeneous Siegel Domains. Journal of Lie Theory, Volume 12 (2002) no. 1, pp. 217-243. doi: 10.5802/jolt.259

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