The Convenient Setting for Quasianalytic Denjoy--Carleman Differentiable Mappings
Abstract
For quasianalytic Denjoy--Carleman differentiable function classes CQ where the weight sequence Q=(Qk) is log-convex, stable under derivations, of moderate growth and also an L-intersection (see 1.6), we prove the following: The category of CQ-mappings is cartesian closed in the sense that CQ(E,CQ(F,G)) CQ(E× F, G) for convenient vector spaces. Applications to manifolds of mappings are given: The group of CQ-diffeomorphisms is a regular CQ-Lie group but not better.
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