Characterizations of algebras of rapidly decreasing generalized functions

Abstract

The well-known characterizations of Schwartz space $\mathcal{S}$ of rapidly decreasing functions is extended to the algebra ${\mathcal{G}}_{\mathcal{S}}$ of rapidly decreasing generalized functions and to the algebra $\mathcal{G}_{% \mathcal{S}}^{\infty}$ of regular rapidly decreasing generalized functions.