On Yamamuro's inverse and implicit function theorems in terms of calibrations

Details On Yamamuro's inverse and implicit function theorems in terms of calibrations On Yamamuro's inverse and implicit function theorems in terms of calibrations

2007-09-25

arxiv.org/abs/0709.3986v5

Mathematics

Functional Analysis

Comments: 9 pages, AmSLaTeX; versions 2--5: correction of minor mistakes

Scientific paper

For the Frechet space E=C^{\infty}(S^1) and for a smooth \phi: R to R, we prove that the associated map E to E given by x mapsto\phi\circ x satisfies the continuous B\Gamma--differentiability condition in Yamamuro's inverse function theorem only if \phi is affine. Via more complicated examples, we also generally discuss the importance of testing the applicability of proposed inverse and implicit function theorems by this kind of simple maps.

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