On the domain of implicit functions in a projective limit setting without additional norm estimates
Functional Analysis
2017-10-31 v1
Abstract
We examine how implicit functions on ILB-Fr\'echet spaces can be obtained without metric or norm estimates which are classically assumed. We obtain implicit functions defined on a domain which is not necessarily open, but which contains the unit open ball of a Banach space. The corresponding inverse functions theorem is obtained, and we finish with an open question on the adequate (generalized) notion of differentiation, needed for the corresponding version of the Fr\"obenius theorem.
Cite
@article{arxiv.1710.11076,
title = {On the domain of implicit functions in a projective limit setting without additional norm estimates},
author = {Jean-Pierre Magnot},
journal= {arXiv preprint arXiv:1710.11076},
year = {2017}
}