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

TL;DR

This paper introduces and analyzes the space of multipliers for the ultradifferentiable rapidly decreasing functions, establishing its properties and topological structures within the framework of Beurling type ultradifferentiability.

Contribution

It defines the multiplier space $\

Findings

Characterization of the space $\\mathcal{O}_{M,\\omega}(\\mathbb{R}^N)$

Analysis of its topological properties

Comparison of different lc-topologies on the space

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.