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

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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https://hal.archives-ouvertes.fr/hal-01626434
Contributor : Jean-Pierre Magnot <>
Submitted on : Monday, October 30, 2017 - 6:28:42 PM
Last modification on : Wednesday, December 19, 2018 - 2:08:04 PM
Document(s) archivé(s) le : Wednesday, January 31, 2018 - 1:41:18 PM

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Jean-Pierre Magnot. On the domain of implicit functions in a projective limit setting without additionnal norm estimates. 2017. ⟨hal-01626434⟩

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