The convenient setting for non-quasianalytic Denjoy–Carleman differentiable mappings☆

By Andreas Kriegl, Peter W. Michor, A. Rainer. 2008

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Abstract 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 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 ) ) ≅ C Q ( E × 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.

View Paper: https://www.semanticscholar.org/paper/00b2294d1901f96d291ab50c33849b2755dc0520

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1. G. Schindl
2. A. Rainer

Citations in the corpus

• Composition in ultradifferentiable classes (2012, methodology): “For these classes we have developed a calculus in infinite dimensions beyond Banach spaces in [24, 26, 25] which is heavily based on composition: A smooth mapping f is of class E{M} if and only if f ◦ p ∈ E{M} for all E{M} Banach plots (i.”