Multipliers on ${\mathcal{S}}_{\omega }({\mathbb{R}}^N)$

Abstract

The aim of this paper is to introduce and to study the space ${\mathcal{O}}_{M,\omega }({\mathbb{R}}^N)$ of the multipliers of the space ${\mathcal{S}}_{\omega }({\mathbb{R}}^N)$ of the $\omega$-ultradifferentiable rapidly decreasing functions of Beurling type. We determine various properties of the space ${\mathcal{O}}_{M,\omega }({\mathbb{R}}^N)$. Moreover, we define and compare some lc-topologies of which ${\mathcal{O}}_{M,\omega }({\mathbb{R}}^N)$ can be naturally endowed.