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

IF 0.7 3区 数学 Q2 MATHEMATICS
A. Debrouwere, L. Neyt
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引用次数: 0

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.
关于超可微函数加权PLB空间桶性的一个注记
在这篇文章中,我们考虑了超可微函数的加权$(PLB)$-空间,这些超可微函数是由一个权重函数和一个权重系统定义的,正如我们在之前的工作[4]中所介绍的那样。我们在定义重量系统方面提供了这些空间何时是超声和桶形的完整表征,从而改进了[4]的主要定理5.1。特别地,我们得到了Beurling型的Gelfand-Shilov空间$\Sigma^{r}_{s}(\mathbb{r}} {d})$的乘子空间是超链的,而Roumieu型的Gelfand-Shilov空间$\mathcal{s} ^{r}_{s}(\mathbb{r}} {d})$的乘子空间不是桶状的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.80
自引率
0.00%
发文量
16
审稿时长
>12 weeks
期刊介绍: The Journal of Analysis and its Applications aims at disseminating theoretical knowledge in the field of analysis and, at the same time, cultivating and extending its applications. To this end, it publishes research articles on differential equations and variational problems, functional analysis and operator theory together with their theoretical foundations and their applications – within mathematics, physics and other disciplines of the exact sciences.
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