  In this article we study standard subspaces of Hilbert spaces of
vector-valued holomorphic functions on tube domains E + i C^0, where C \subeq E
is a pointed generating cone invariant under e^{R h} for some endomorphism h
\in \End(E), diagonalizable with the eigenvalues 1,0,-1 (generalizing a Lorentz
boost). This data specifies a wedge domain W(E,C,h) \subeq E and one of our
main results exhibits corresponding standard subspaces as being generated using
test functions on these domains. We also investigate aspects of reflection
positivity for the triple (E,C,e^{\pi i h}) and the support properties of
distributions on E, arising as Fourier transforms of operator-valued measures
defining the Hilbert spaces H. For the imaginary part of these distributions,
we find similarities to the well known Huygens' principle, relating to wedge
duality in the Minkowski context. Interesting examples are the Riesz
distributions associated to euclidean Jordan algebras.
