On the Projective Description of Spaces of Ultradifferentiable Functions of Roumieu Type

Abstract

We provide a projective description of the space (formula presented) of ultradifferentiable functions of Roumieu type, where Ω is an arbitrary open set in (formula presented) is a weight matrix satisfying the analogue of Komatsu’s condition (M.2)′. 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.