Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4591719 | Journal of Functional Analysis | 2009 | 35 Pages |
Abstract
For Denjoy–Carleman differentiable function classes CM 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 CM if it maps CM-curves to CM-curves. The category of CM-mappings is cartesian closed in the sense that CM(E,CM(F,G))≅CM(E×F,G) for convenient vector spaces. Applications to manifolds of mappings are given: The group of CM-diffeomorphisms is a CM-Lie group but not better.
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