Inverse Function Theorems for Generalized Smooth Functions

Chapter

Abstract

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 smooth functions and prove both the local and some global inverse function theorems.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.University of ViennaWienAustria

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