论文标题
a $ \ Mathcal {C}^k $ -seeley-Extension-theorem用于Bastiani的差分微积分
A $\mathcal{C}^k$-Seeley-Extension-Theorem for Bastiani's Differential Calculus
论文作者
论文摘要
我们将Seeley在Bastiani差分计算的背景下概括为无限维度的经典扩展结果。该结构遵循Seeley的原始方法，但不仅涉及$ C^k $ -maps（对于$ k \ in \ Mathbb {n} \ cup \ cup \ {\ fist \ {\ infty \} $）（一半空间的子集）被延长，而且还延长了差异的差异，而且在某些情况下，其差异不断地延伸到某些情况下的边界。概括的另一个特征是，我们构建了满足某些兼容性（和连续性）条件的扩展运算符（而不是一个单个扩展运算符）的家族。也讨论了各种应用程序。
We generalize a classical extension result by Seeley in the context of Bastiani's differential calculus to infinite dimensions. The construction follows Seeley's original approach, but is significantly more involved as not only $C^k$-maps (for $k\in \mathbb{N}\cup\{\infty\}$) on (subsets of) half spaces are extended, but also continuous extensions of their differentials to some given piece of boundary of the domains under consideration. A further feature of the generalization is that we construct families of extension operators (instead of only one single extension operator) that fulfill certain compatibility (and continuity) conditions. Various applications are discussed as well.
