The Convenient Setting for Non-quasianalytic Denjoy–carleman Differentiable Mappings
نویسندگان
چکیده
For Denjoy–Carleman differential function classes C where the weight sequence M = (Mk) is logarithmically convex, stable under derivations, and non-quasianalytic of moderate growth, we prove the following: A mapping is C if it maps C -curves to C -curves. The category of C -mappings is cartesian closed in the sense that C (E, C (F, G)) = C (E × F, G) for convenient vector spaces. Applications to manifolds of mappings are given: The group of C -diffeomorphisms is a C -Lie group but not better.
منابع مشابه
To appear in J. Functional Analysis THE CONVENIENT SETTING FOR NON-QUASIANALYTIC DENJOY–CARLEMAN DIFFERENTIABLE MAPPINGS
For Denjoy–Carleman differentiable function classes C where the weight sequence M = (Mk) is logarithmically convex, stable under derivations, and non-quasianalytic of moderate growth, we prove the following: A mapping is C if it maps C -curves to C -curves. The category of C -mappings is cartesian closed in the sense that C (E, C (F, G)) = C (E × F, G) for convenient vector spaces. Applications...
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