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

Autor:	Kriegl, Andreas, Michor, Peter W., Rainer, Armin
Rok vydání:	2008
Předmět:	Mathematics - Functional Analysis Mathematics - Classical Analysis and ODEs 26E10 46A17 46E50 58B10 58B25 58C25 58D05 58D15
Zdroj:	J. Functional Analysis 256 (2009), 3510-3544
Druh dokumentu:	Working Paper
DOI:	10.1016/j.jfa.2009.03.003.x
Popis:	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. Comment: LaTeX, 29 pages, Some misprints corrected. Again some misprints corrected
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0804.2995 Zobrazit plný text záznamu View this record from Arxiv