A version of scale calculus and the associated Fredholm theory
arXiv:1602.07108
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.
131 pages; v2: typos corrected, references added for section 1; v3: typos corrected, added Section 5.3 on finite dimensional reduction and Sard-Smale; v4: significantly expanded Section 4, added Section 6, Summary