论文标题
Banach太空函数的类别
A Category of Banach Space Functors
论文作者
论文摘要
我们在功能分析上介绍了用于无限尺寸谎言组动作的功能分析的理论观点。我们为Banach有价值的函子开发了功能性计算，尤其是证明了某些类别的运算符的指数映射存在，这些操作员概括了一阶部分差分运算符。该代数框架可用于动态系统和KAM理论，以提供正常形式和广泛的变形。它用于我们的有关该主题的论文中，例如Herman猜想纸，Vector Fields等的多种变形定理。
We introduce a sheaf theoretic viewpoint on functional analysis designed for infinite dimensional Lie group actions. We develop functional calculus for Banach valued functors and, in particular, prove the existence of an exponential map for a certain class of operators that generalise first order partial differential operators. This algebraic framework can be used in dynamical systems and KAM theory to provide normal forms and versal deformations. it is used in our papers on the subject such as the Herman conjecture paper, the versal deformation theorem for vector fields etc.
