论文标题
与$（\ Mathbb {r}^{d}，+）$相关的Denjoy-Carleman类中的分解。
Factorization in Denjoy-Carleman classes associated to representations of $(\mathbb{R}^{d},+)$
论文作者
论文摘要
对于两种类型的中等增长表示形式，$（\ Mathbb {r}^d，+）$依次完成局部凸出的Hausdorff空间（包括F-陈述[J. funct.262（2012），667-681]它们尤其是我们的分解定理[sublyem salization。
For two types of moderate growth representations of $(\mathbb{R}^d,+)$ on sequentially complete locally convex Hausdorff spaces (including F-representations [J. Funct. Anal. 262 (2012), 667-681], we introduce Denjoy-Carleman classes of ultradifferentiable vectors and show a strong factorization theorem of Dixmier-Malliavin type for them. In particular, our factorization theorem solves [Conjecture 6.; J. Funct. Anal. 262 (2012), 667-681] for analytic vectors of representations of $G =(\mathbb{R}^d,+)$. As an application, we show that various convolution algebras and modules of ultradifferentiable functions satisfy the strong factorization property.
