An inverse function theorem for Colombeau tame Frolicher-Kriegl maps

Details An inverse function theorem for Colombeau tame Frolicher-Kriegl maps An inverse function theorem for Colombeau tame Frolicher-Kriegl maps

2007-03-05

arxiv.org/abs/math/0703092v5

Mathematics

Functional Analysis

AmSLaTeX, 8 pages; v2: scope of Corollary 9 extended, misprints corrected; v3: inaccuracies in 3 Def:s, misprints corrected, r

Scientific paper

For 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.

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