  A regular sampling theory in a multiply generated unitary invariant subspace
of a separable Hilbert space $\mathcal{H}$ is proposed. This subspace is
associated to a unitary representation of a countable discrete abelian group
$G$ on $\mathcal{H}$. The samples are defined by means of a filtering process
which generalizes the usual sampling settings. The multiply generated setting
allows to consider some examples where the group $G$ is non-abelian as, for
instance, crystallographic groups. Finally, it is worth to mention that
classical average or pointwise sampling in shift-invariant subspaces are
particular examples included in the followed approach.
