An inverse function theorem for Colombeau tame Frolicher-Kriegl maps

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dc.creatorHiltunen, Seppo I.
dc.date2007-03-05
dc.date2007-03-22
dc.date.accessioned2026-07-07T07:53:04Z
dc.date.available2026-07-07T07:53:04Z
dc.descriptionFor k=1,2,... infty and a Frolicher-Kriegl order k Lipschitz differentiable map f:E supseteq U to E having derivative at x_0 in U a linear homeomorphism E to E and satisfying a Colombeau type tameness condition, we prove that x_0 has a neighborhood V subseteq U with f|V a local order k Lipschitz diffeomorphism. As a corollary we obtain a similar result for Keller C_c^{\infty} maps with E in a class including Frechet and Silva spaces. We also indicate a procedure for verifying the tameness condition for maps of the type x mapsto varphi circ [id,x] and spaces E=C^{\infty}(Q) when Q is compact by considering the case Q=[0,1]. Our considerations are motivated by the wish to try to retain something valuable in an interesting but defective treatment of integrability of Lie algebras by J. Leslie.
dc.descriptionAmSLaTeX, 8 pages; v2: scope of Corollary 9 extended, misprints corrected; v3: inaccuracies in 3 Def:s, misprints corrected, reorganization of proofs suggested in the former footnote; v4: minor specifications added, misprints corrected; v5: a forgotten detail added in the proof of 10 Prop., minor rewording in the proof of 8 Thm
dc.identifierhttps://arxiv.org/abs/math/0703092
dc.identifierhttp://arxiv.org/abs/math/0703092
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/126112
dc.subjectFunctional Analysis
dc.subject58C15, 46A61, 46T20
dc.titleAn inverse function theorem for Colombeau tame Frolicher-Kriegl maps
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