Subject: Mathematics - Functional Analysis
Subject: Mathematics - Functional Analysis
Subject: Primary 42A85, 46E10, 46E25, Secondary 46F05, 46H05

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Year: 2021

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Type: Journal Article

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Title: Factorization in Denjoy-Carleman classes associated to representations of $(\\mathbb{R}^{d},+)$

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Author: Andreas Debrouwere
Author: Prangoski, Bojan
Author: Jasson Vindas

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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.

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Publisher: Elsevier BV

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Relation: J. Funct. Anal. 280 (2021), Article 108831 (31 pages)

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Identifier: oai:repository.ukim.mk:20.500.12188/20081
Identifier: http://hdl.handle.net/20.500.12188/20081
Identifier: 10.1016/j.jfa.2020.108831
Identifier: https://api.elsevier.com/content/article/PII:S0022123620303748?httpAccept=text/xml
Identifier: https://api.elsevier.com/content/article/PII:S0022123620303748?httpAccept=text/plain
Identifier: 280
Identifier: 3

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