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

2007/09/25 by Seppo I. Hiltunen, Hiltunen, Seppo I.
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Numerical methods in inverse problems #Stability and Controllability of Differential Equations #math.FA #msc:35A05 #msc:35B30 #msc:46G05 #msc:46T20 #msc:47J07 #msc:58C15 #msc:58D05

paper · pdf · doi:10.48550/arxiv.0709.3986

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

arxiv created 2007/12/21 · arxiv updated 2011/11/09

Abstract

For the Frechet space E=C^∞(S¹) and for a smooth ϕ: R to R, we prove that the associated map E to E given by x mapstoϕ∘ 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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