# The Convenient Setting for Quasianalytic Denjoy-Carleman Differentiable Mappings - Mathematics > Functional Analysis

Abstract: For quasianalytic Denjoy-Carleman differentiable function classes $C^Q$where the weight sequence $Q=Q k$ is log-convex, stable under derivations, ofmoderate growth and also an $\mathcal L$-intersection see 1.6, we prove thefollowing: The category of $C^Q$-mappings is cartesian closed in the sense that$C^QE,C^QF,G\cong C^QE\times F, G$ for convenient vector spaces.Applications to manifolds of mappings are given: The group of$C^Q$-diffeomorphisms is a regular $C^Q$-Lie group but not better.

Author: Andreas Kriegl, Peter W. Michor, Armin Rainer

Source: https://arxiv.org/