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arXiv · 2206.10252

A note on the barrelledness of weighted $(PLB)$-spaces of ultradifferentiable functions

Andreas Debrouwere·Lenny Neyt
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Abstract

In this note we consider weighted $(PLB)$-spaces of ultradifferentiable functions defined via a weight function and a weight system, as introduced in our previous work [4]. We provide a complete characterization of when these spaces are ultrabornological and barrelled in terms of the defining weight system, thereby improving the main Theorem 5.1 of [4]. In particular, we obtain that the multiplier space of the Gelfand-Shilov space $\Sigma^{r}_{s}(\mathbb{R}^{d})$ of Beurling type is ultrabornological, whereas the one of the Gelfand-Shilov space $\mathcal{S}^{r}_{s}(\mathbb{R}^{d})$ of Roumieu type is not barrelled.

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Andreas Debrouwere, Lenny Neyt. 2022-06-21. A note on the barrelledness of weighted $(PLB)$-spaces of ultradifferentiable functions. https://arxiv.org/abs/2206.10252

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