Inverse Function Theorems for Generalized Smooth Functions

@article{Giordano2016InverseFT,
  title={Inverse Function Theorems for Generalized Smooth Functions},
  author={Paolo Giordano and Michael Kunzinger},
  journal={arXiv: Functional Analysis},
  year={2016},
  pages={95-114}
}
Generalized smooth functions are a possible formalization of the original historical approach followed by Cauchy, Poisson, Kirchhoff, Helmholtz, Kelvin, Heaviside, and Dirac to deal with generalized functions. They are set-theoretical functions defined on a natural non-Archimedean ring, and include Colombeau generalized functions (and hence also Schwartz distributions) as a particular case. One of their key property is the closure with respect to composition. We review the theory of generalized… 

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