Characterization of the Moyal Multiplier Algebras for the Generalized Spaces of Type S

Abstract

We investigate the properties of the Moyal multiplier algebras for the generalized Gelfand-Shilov spaces $$S_{{a_k}}^{{b_n}}$$ . We prove that these algebras contain Palamodov spaces of type $${\mathscr{E}}$$ , and establish continuity properties of the operators with Weyl symbols in this class. Analogous results are obtained for the projective version of the spaces of type S and are extended to the multiplier algebras for various translation-invariant star products.