标题： 标度微积分的一个版本及相关弗雷德霍姆理论 显示英文标题

标题： A version of scale calculus and the associated Fredholm theory

摘要： 本文提供了一种针对特定类型弗雷歇空间之间（非线性）弗雷德霍姆映射概念的尺度微积分版本，尽可能保留弗雷德霍姆映射在巴拿赫空间之间所享有的性质，并且此类映射存在一个常秩定理。它是通过将[HWZ14]和[Weh12]中的线性弗雷德霍姆映射概念扩展到可以应用纳什-莫斯逆函数定理的设置，并且也涵盖了必要的例子，如重新参数化作用和（非线性）椭圆偏微分算子。 显示英文摘要

摘要： This article provides a version of scale calculus geared towards a notion of (nonlinear) Fredholm maps between certain types of Frechet spaces, retaining as many as possible of the properties Fredholm maps between Banach spaces enjoy, and the existence of a constant rank theorem for such maps. It does so by extending the notion of linear Fredholm maps from [HWZ14] and [Weh12] to a setting where the Nash-Moser inverse function theorem can be applied and which also encompasses the necessary examples such as the reparametrisation action and (nonlinear) elliptic partial differential operators.