The complex crown for homogeneous harmonic spaces

Camporesi, Roberto; Krötz, Bernhard

doi:10.1090/S0002-9947-2011-05571-6

The complex crown for homogeneous harmonic spaces
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by Roberto Camporesi and Bernhard Krötz

Trans. Amer. Math. Soc. 364 (2012), 2227-2240

DOI: https://doi.org/10.1090/S0002-9947-2011-05571-6

Published electronically: December 1, 2011

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Abstract:

The complex crown of a noncompact Riemannian symmetric space $X=G/K$ is generalized to the case of homogeneous harmonic spaces $S=NA$. We prove that every eigenfunction of the Laplace-Beltrami operator on $S$ extends holomorphically to the crown, and that the crown is the maximal $S$-invariant domain in $S_{\mathbb {C}}$ with this property.

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