On the projective description of spaces of ultradifferentiable functions of Roumieu type

Abstract

We provide a projective description of the space ${\mathcal{E}}^{\{\mathfrak{M}\}}(\Omega )$ of ultradifferentiable functions of Roumieu type, where $\Omega$ is an arbitrary open set in ${\mathbb{R}}^d$ and $\mathfrak{M}$ is a weight matrix satisfying the analogue of Komatsu's condition $(M.2{)}^{\prime }$. In particular, we obtain in a unified way projective descriptions of ultradifferentiable classes defined via a single weight sequence (Denjoy-Carleman approach) and via a weight function (Braun-Meise-Taylor approach) under considerably weaker assumptions than in earlier versions of these results.

8 pages

Cited by in corpus (1)

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