  We provide an abstract framework for the study of certain spectral properties
of parabolic systems; specifically, we determine under which general conditions
to expect the presence of absolutely continuous spectral measures. We use these
general conditions to derive results for spectral properties of time-changes of
unipotent flows on homogeneous spaces of semisimple groups regarding absolutely
continuous spectrum as well as maximal spectral type; the time-changes of the
horocycle flow are special cases of this general category of flows. In addition
we use the general conditions to derive spectral results for twisted horocycle
flows and to rederive certain spectral results for skew products over
translations and Furstenberg transformations.
