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

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.