The Dixmier-Malliavin Theorem and Bornological Vector Spaces

Abstract

This note is intended to reformulate the Dixmier-Malliavin theorem about smooth group representations in the language of bornological vector spaces, instead of topological vector spaces. This language turns out to allow a more general theorem to be proven, and we are able to use it to strengthen a result of Meyer from arXiv:math/0310094. This paper is based on a part of the author's thesis.

References in corpus (1)

• Embeddings of derived categories of bornological modules

Cited by in corpus (2)

• Modules of Zeta Integrals for $\mathrm{GL}(1)$
• Schwartz functions, Hadamard products, and the Dixmier-Malliavin theorem