The Convenient Setting for Quasianalytic Denjoy--Carleman Differentiable Mappings

Details The Convenient Setting for Quasianalytic Denjoy--Carleman Differentiable Mappings The Convenient Setting for Quasianalytic Denjoy--Carleman Differentiable Mappings

2009-09-30

arxiv.org/abs/0909.5632v2

J. Functional Analysis 261, 7 (2011) 1799-1834

Mathematics

Functional Analysis

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

Scientific paper

10.1016/j.jfa2011.05.019

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 $\mathcal L$-intersection (see 1.6), we prove the following: The category of $C^Q$-mappings is cartesian closed in the sense that $C^Q(E,C^Q(F,G))\cong C^Q(E\times F, G)$ 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.

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