  We prove that the Moyal multiplier algebras of the generalized Gelfand-Shilov
spaces of type $S$ contain Palamodov spaces of type $\mathcal E$ and the
inclusion maps are continuous. We also give a direct proof that the Palamodov
spaces are algebraically and topologically isomorphic to the strong duals of
the spaces of convolutors for the corresponding spaces of type $S$. The
obtained results provide an effective way to describe the properties of
pseudodifferential operators with symbols in the spaces of type $\mathcal E$.
