The complex crown for homogeneous harmonic spaces
The complex crown for homogeneous harmonic spaces
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 …