Implicit functions from topological vector spaces to Fréchet spaces in the presence of metric estimates

Details Implicit functions from topological vector spaces to Fréchet spaces in the presence of metric estimates Implicit functions from topological vector spaces to Fréchet spaces in the presence of metric estimates

2006-12-22

arxiv.org/abs/math/0612673v5

Mathematics

Functional Analysis

51 pages, LaTeX (v5: revision of introduction)

Scientific paper

We prove an implicit function theorem for Keller C^k_c-maps from arbitrary real or complex topological vector spaces to Frechet spaces, imposing only a certain metric estimate on the partial differentials. As a tool, we show the C^k-dependence of fixed points on parameters for suitable families of contractions of a Frechet space. The investigations were stimulated by a recent metric approach to differentiability in Frechet spaces by Olaf Mueller. Our results also subsume generalizations of Mueller's Inverse Function Theorem for mappings between Frechet spaces. As an application, we prove existence and uniqueness of solutions to suitable ordinary differential equations in Frechet spaces, and study their dependence on initial conditions and parameters.

Affiliated with

Also associated with

No associations

Rating

Implicit functions from topological vector spaces to Fréchet spaces in the presence of metric estimates does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Implicit functions from topological vector spaces to Fréchet spaces in the presence of metric estimates, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Implicit functions from topological vector spaces to Fréchet spaces in the presence of metric estimates will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-531657