On Yamamuro's inverse and implicit function theorems in terms of calibrations
arXiv:0709.3986
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.
Comments: 9 pages, AmSLaTeX; versions 2--5: correction of minor mistakes