Abstract For two types of moderate growth representations of ( R d , + ) on sequentially complete locally convex Hausdorff spaces (including F-representations [14] ), 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 [14, Conjecture 6.4] for analytic vectors of representations of G = ( R d , + ) . As an application, we show that various convolution algebras and modules of ultradifferentiable functions satisfy the strong factorization property.

中文翻译：

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与 (Rd,+) 的表示相关的 Denjoy-Carleman 类中的因式分解

摘要 对于 (R d , + ) 在顺序完全局部凸 Hausdorff 空间（包括 F 表示 [14] ）上的两种中等增长表示，我们引入了超微向量的 Denjoy-Carleman 类，并展示了 Dixmier- Malliavin 类型为他们。特别是，我们的分解定理解决了 [14, Conjecture 6.4] 表示 G = ( R d , + ) 的解析向量。作为一个应用，我们展示了各种卷积代数和超微函数模块满足强分解特性。