Beurling型和Roumieu型Denjoy-Carleman微分映射的方便设置
The Convenient Setting for Denjoy--Carleman Differentiable Mappings of Beurling and Roumieu Type
摘要：
我们证明了在一个统一的方式，所有Denjoy-Carleman可微函数类的Beurling型$C^{(M)}$和Roumieu型$C^{\{M\}}$，承认一个方便的设置，如果重量序列$M=(M_k)$是对数凸的和适度的增长：对于$\mathcal C$表示$C^{(M)}$或$C^{\{M\}}$，范畴的$\mathcal C$ -映射是carlington封闭的意义下，$\mathcal C(E,\mathcal C(F,G))\cong \mathcal C(E\times F, G)$方便的向量空间。给出了在映射流形上的应用：若$\mathcal C \supseteq C^ω$为正则$\mathcal C$ -李群，则$\mathcal C$ -李群是正则的.
英文摘要：
We prove in a uniform way that all Denjoy--Carleman differentiable function classes of Beurling type $C^{(M)}$ and of Roumieu type $C^{\{M\}}$, admit a convenient setting if the weight sequence $M=(M_k)$ is log-convex and of moderate growth: For $\mathcal C$ denoting either $C^{(M)}$ or $C^{\{M\}}$, the category of $\mathcal C$-mappings is cartesian closed in the sense that $\mathcal C(E,\mathcal C(F,G))\cong \mathcal C(E\times F, G)$ for convenient vector spaces. Applications to manifolds of mappings are given: The group of $\mathcal C$-diffeomorphisms is a regular $\mathcal C$-Lie group if $\mathcal C \supseteq C^ω$, but not better.
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