On the domain of implicit functions in a projective limit setting without additional norm estimates

2017/10/30 by Jean-Pierre Magnot, Magnot, Jean-Pierre
Computer Science · Engineering · Mathematics · #58C15 #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis #Stability and Controllability of Differential Equations #math.FA #msc:58C15

paper · pdf · doi:10.48550/arxiv.1710.11076

arxiv created 2017/10/30 · openalex publication_date 2017/10/30 · arxiv updated 2017/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We examine how implicit functions on ILB-Fréchet spaces can be obtained without metric or norm estimates which are classically assumed. We obtain implicit functions defined on a domain D 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 Fröbenius theorem.

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