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

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

2008-04-18

arxiv.org/abs/0804.2995v3

J. Functional Analysis 256 (2009), 3510-3544

Mathematics

Functional Analysis

LaTeX, 29 pages, Some misprints corrected. Again some misprints corrected

Scientific paper

10.1016/j.jfa.2009.03.003.x

For Denjoy--Carleman differential function classes $C^M$ where the weight sequence $M=(M_k)$ is logarithmically convex, stable under derivations, and non-quasianalytic of moderate growth, we prove the following: A mapping is $C^M$ if it maps $C^M$-curves to $C^M$-curves. The category of $C^M$-mappings is cartesian closed in the sense that $C^M(E,C^M(F,G))\cong C^M(E\x F, G)$ for convenient vector spaces. Applications to manifolds of mappings are given: The group of $C^M$-diffeomorphisms is a $C^M$-Lie group but not better.

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