  We construct valuations on the space of finite-valued convex functions using
integration of differential forms over the differential cycle associated to a
convex function. We describe the kernel of this procedure and show that the
intersection of this space of smooth valuations with the space of all
continuous dually epi-translation invariant valuations on convex functions is
dense in the latter. As an application, we obtain a description of
1-homogeneous, continuous, dually epi-translation invariant valuations that are
invariant with respect to a compact subgroup operating transitively on the unit
sphere.
