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A new higher order chain rule and Gevrey class. (English) Zbl 0719.58002
From the author’s abstract: “A new higher order chain rule both in the sense of ordinary functions and in the sense of Fréchet derivatives is given. It is applied to prove that a composite map of Gevrey maps is again Gevrey. An inverse map theorem etc. are also given in the framework of Gevrey maps.”
Reviewer: N.Jacob (Erlangen)

58C25 Differentiable maps on manifolds
46G05 Derivatives of functions in infinite-dimensional spaces
58J99 Partial differential equations on manifolds; differential operators
26A24 Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems
58C15 Implicit function theorems; global Newton methods on manifolds
Full Text: DOI
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