On Yamamuro's inverse and implicit function theorems in terms of calibrations
On Yamamuro's inverse and implicit function theorems in terms of calibrations
For the Frechet space E=C^{\infty}(S^1) and for a smooth ��: R to R, we prove that the associated map E to E given by x mapsto��\circ x satisfies the continuous B��--differentiability condition in Yamamuro's inverse function theorem only if ��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.
Comments: 9 pages, AmSLaTeX; versions 2--5: correction of minor mistakes
Mathematics - Functional Analysis, 58C15, 35B30, 58D05, 35A05 (Secondary), 46T20, 47J07, 46G05 (Primary), FOS: Mathematics, Functional Analysis (math.FA), 46T20, 47J07, 46G05 (Primary); 58C15, 35B30, 58D05, 35A05 (Secondary)
Mathematics - Functional Analysis, 58C15, 35B30, 58D05, 35A05 (Secondary), 46T20, 47J07, 46G05 (Primary), FOS: Mathematics, Functional Analysis (math.FA), 46T20, 47J07, 46G05 (Primary); 58C15, 35B30, 58D05, 35A05 (Secondary)
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