Factorization in Denjoy-Carleman classes associated to representations of $(\mathbb{R}^{d},+)$
Journal
J. Funct. Anal. 280 (2021), Article 108831 (31 pages)
Date Issued
2021
Author(s)
Andreas Debrouwere
Jasson Vindas
DOI
10.1016/j.jfa.2020.108831
Abstract
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.
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.