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Title: Factorization in Denjoy-Carleman classes associated to representations of $(\mathbb{R}^{d},+)$
Authors: Andreas Debrouwere
Prangoski, Bojan 
Jasson Vindas
Keywords: Mathematics - Functional Analysis
Mathematics - Functional Analysis
Primary 42A85, 46E10, 46E25, Secondary 46F05, 46H05
Issue Date: 2021
Publisher: Elsevier BV
Journal: J. Funct. Anal. 280 (2021), Article 108831 (31 pages)
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.
DOI: 10.1016/j.jfa.2020.108831
Appears in Collections:Faculty of Mechanical Engineering: Journal Articles

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