The Convenient Setting for Quasianalytic Denjoy--Carleman Differentiable Mappings

Andreas Kriegl; Peter W. Michor; Armin Rainer

doi:10.1016/j.jfa2011.05.019

paper

The Convenient Setting for Quasianalytic Denjoy--Carleman Differentiable Mappings

arXiv:0909.5632 · doi:10.1016/j.jfa2011.05.019

Abstract

For quasianalytic Denjoy--Carleman differentiable function classes $C^{Q}$ where the weight sequence $Q = (Q_{k})$ is log-convex, stable under derivations, of moderate growth and also an $L$ -intersection (see 1.6), we prove the following: The category of $C^{Q}$ -mappings is cartesian closed in the sense that $C^{Q} (E, C^{Q} (F, G)) ≅ C^{Q} (E \times F, G)$ 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.

29 pages. Some typos corrected; J. Functional Analysis (2011)