English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

In this paper we continue the study of the spaces$\mathcal{O}_{M,\omega}(\mathbb{R}^N)$ and$\mathcal{O}_{C,\omega}(\mathbb{R}^N)$ undertaken in [1]. We determine newrepresentations of such spaces and we give some structure theorems for theirdual spaces. Furthermore, we show that $\mathcal{O}'_{C,\omega}(\mathbb{R}^N)$is the space of convolutors of the space $\mathcal{S}_\omega(\mathbb{R}^N)$ ofthe $\omega$-ultradifferentiable rapidly decreasing functions of Beurling type(in the sense of Braun, Meise and Taylor) and of its dual space$\mathcal{S}'_\omega(\mathbb{R}^N)$. We also establish that the Fouriertransform is an isomorphism from $\mathcal{O}'_{C,\omega}(\mathbb{R}^N)$ onto$\mathcal{O}_{M,\omega}(\mathbb{R}^N)$. In particular, we prove that thisisomorphism is topological when the former space is endowed with the strongoperator lc-topology induced by$\mathcal{L}_b(\mathcal{S}_\omega(\mathbb{R}^N))$ and the last space is endowedwith its natural lc-topology.

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