Inclusion theorems for the Moyal multiplier algebras of generalized Gelfand-Shilov spaces

TL;DR

This paper establishes the inclusion of Palamodov spaces within Moyal multiplier algebras of generalized Gelfand-Shilov spaces, providing insights into pseudodifferential operators with symbols in these spaces.

Contribution

It proves the continuous inclusion of Palamodov spaces into Moyal multiplier algebras and shows their isomorphism to duals of spaces of convolutors, advancing the understanding of these function spaces.

Findings

Palamodov spaces are contained in Moyal multiplier algebras.

The inclusion maps are continuous.

Palamodov spaces are isomorphic to duals of convolutor spaces.

Abstract

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 $\mathcal E$.