The structure of spaces of quasianalytic functions of Roumieu type

Abstract

It is shown that spaces of quasianalytic ultradifferentiable functions of Roumieu type ℰ{w}(Ω), on an open convex set $$(\Omega)\,{\subseteq}\,{\mathbb{R}}^d$$ , satisfy some new (Ω) -type linear topological invariants. Some consequences for the splitting of short exact sequences of these spaces as well as for the structure of the spaces are derived. In particular, Frechet quotients of ℰ{w}(Ω) have property ( $$\overline{\overline \Omega}$$ ), while dual Frechet quotients have property ( $$\underline{A}$$ ) of Vogt.