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- W4294014705 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." @default.
- W4294014705 created "2022-09-01" @default.
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- W4294014705 creator A5069967448 @default.
- W4294014705 date "2022-06-21" @default.
- W4294014705 modified "2023-10-18" @default.
- W4294014705 title "A note on the barrelledness of weighted $(PLB)$-spaces of ultradifferentiable functions" @default.
- W4294014705 doi "https://doi.org/10.48550/arxiv.2206.10252" @default.
- W4294014705 hasPublicationYear "2022" @default.
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