  We establish a method for constructing equivariant distributions on smooth
real algebraic varieties from equivariant distributions on Zariski open
subsets. This is based on Bernstein's theory of analytic continuation of
holonomic distributions. We use this to construct $H$-equivariant functionals
on principal series representations of $G$, where $G$ is a real reductive group
and $H$ is an algebraic subgroup. We also deduce the existence of generalized
Whittaker models for degenerate principal series representations. As a special
case, this gives short proofs of existence of Whittaker models on principal
series representations, and of analytic continuation of standard intertwining
operators. Finally, we extend our constructions to the $p$-adic case using a
recent result of Hong and Sun.
