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arXiv · 0709.3986

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

Seppo I. Hiltunen
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Abstract

For the Frechet space E=C^{\infty}(S^1) and for a smooth ϕ: R to R, we prove that the associated map E to E given by x mapstoϕ\circ x satisfies the continuous BΓ--differentiability condition in Yamamuro's inverse function theorem only if ϕis 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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BibTeXRIS

Seppo I. Hiltunen. 2007-12-21. On Yamamuro's inverse and implicit function theorems in terms of calibrations. https://arxiv.org/abs/0709.3986

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