论文标题
关于加权$（PLB）$ - 超平整功能的空间的注释
A note on the barrelledness of weighted $(PLB)$-spaces of ultradifferentiable functions
论文作者
论文摘要
在本说明中，我们考虑了加权$（PLB）$ - 通过权重功能和权重系统定义的超平变功能的空间，如我们先前的工作中所述[4]。我们提供了这些空间超生产学何时具有定义重量系统的桶形的完整表征，从而改善了[4]的主要定理5.1。特别是，我们获得了Gelfand-Shilov空间的乘数空间$σ^{r} _ {s}（\ Mathbb {r}^{d}）beurling类型的$是超生产的，而Gelfand-Shilov Space之一$ \ MATHCAL {s}^{r} _ {s}（\ Mathbb {r}^{d}）$ roumieu类型的$没有被桶装。
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 $Σ^{r}_{s}(\mathbb{R}^{d})$ 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.
