度量估计存在下拓扑向量空间到Fréchet空间的隐函数
Implicit functions from topological vector spaces to Fréchet spaces in the presence of metric estimates
摘要：
证明了从任意实或复拓扑向量空间到Frechet空间的Keller C^k_c-映射的一个隐函数定理，仅对偏微分作了一定的度量估计.作为一个工具，我们显示了C^k-依赖的不动点的参数，适当的家庭收缩的Frechet空间。奥拉夫·穆勒（Olaf Mueller）最近对Frechet空间中可微性的度量方法刺激了这些研究。我们的结果也是Mueller关于Frechet空间映射的反函数定理的进一步推广。作为应用，我们证明了Frechet空间中合适的常微分方程解的存在唯一性，并研究了它们对初始条件和参数的依赖性.
英文摘要：
We prove an implicit function theorem for Keller C^k_c-maps from arbitrary real or complex topological vector spaces to Frechet spaces, imposing only a certain metric estimate on the partial differentials. As a tool, we show the C^k-dependence of fixed points on parameters for suitable families of contractions of a Frechet space. The investigations were stimulated by a recent metric approach to differentiability in Frechet spaces by Olaf Mueller. Our results also subsume generalizations of Mueller's Inverse Function Theorem for mappings between Frechet spaces. As an application, we prove existence and uniqueness of solutions to suitable ordinary differential equations in Frechet spaces, and study their dependence on initial conditions and parameters.
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