scholarly journals An inverse function theorem in Fréchet spaces

2011 ◽  
Vol 28 (1) ◽  
pp. 91-105 ◽  
Author(s):  
Ivar Ekeland
Keyword(s):  
Inverse Function ◽  
Inverse Function Theorem ◽  
Fréchet Spaces

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

2020 ◽  
Vol 53 (1) ◽  
pp. 112-120 ◽  
Author(s):  
Jean-Pierre Magnot
Keyword(s):  
Inverse Function ◽  
Projective Limit ◽  
Inverse Function Theorem ◽  
Open Ball ◽  
Fréchet Spaces ◽  
Implicit Functions ◽  
Frobenius Theorem ◽  
Norm Estimates ◽  
Limit Setting ◽  
Open Question

AbstractWe 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 function 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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