Finite order differentiability properties, fixed points and implicit functions over valued fields

Details Finite order differentiability properties, fixed points and implicit functions over valued fields Finite order differentiability properties, fixed points and implicit functions over valued fields

2005-11-08

arxiv.org/abs/math/0511218v2

Mathematics

Functional Analysis

LaTeX, 59 pages, broadly written preprint (v2: new Appendix C extends C^1-case from locally compact fields to complete valued

Scientific paper

We prove an implicit function theorem for C^k-maps from arbitrary topological vector spaces over valued fields to Banach spaces (for k at least 2). As a tool, we show the C^k-dependence of fixed points on parameters for suitable families of contractions of a Banach space. Similar results are obtained for k times strictly differentiable maps, and for k times Lipschitz differentiable maps. In the real case, our results subsume an implicit function theorem for Keller C^k_c-maps from arbitrary topological vector spaces to Banach spaces.

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