  Let G/H be a semisimple symmetric space. The main tool to embed a principal
series representation of G into L^2(G/H) are the H-invariant distribution
vectors. If G/H is a non-compactly causal symmetric space, then G/H can be
realized as a boundary component of the complex crown $\Xi$. In this article we
construct a minimal G-invariant subdomain $\Xi_H$ of $\Xi$ with G/H as Shilov
boundary. Let $\pi$ be a spherical principal series representation of G. We
show that the space of H-invariant distribution vectors of $\pi$, which admit a
holomorphic extension to $\Xi_H$, is one dimensional. Furthermore we give a
spectral definition of a Hardy space corresponding to those distribution
vectors. In particular we achieve a geometric realization of a multiplicity
free subspace of L^2(G/H)_mc in a space of holomorphic functions.
