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Journal Articles Demonstratio Mathematica Year : 2020

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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Dates and versions

hal-01626434 , version 1 (30-10-2017)

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  • HAL Id : hal-01626434 , version 1

Cite

Jean-Pierre Magnot. On the domain of implicit functions in a projective limit setting without additionnal norm estimates. Demonstratio Mathematica, 2020, 53 (1), pp.112-120. ⟨hal-01626434⟩
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