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

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