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arXiv · 1602.07108

A version of scale calculus and the associated Fredholm theory

Andreas Gerstenberger
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Abstract

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.

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Andreas Gerstenberger. 2016-02-23. A version of scale calculus and the associated Fredholm theory. https://arxiv.org/abs/1602.07108

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