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arXiv · 1602.00013

Inverse Function Theorems for Generalized Smooth Functions

Paolo Giordano·Michael Kunzinger
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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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BibTeXRIS

Paolo Giordano, Michael Kunzinger. 2016-06-13. Inverse Function Theorems for Generalized Smooth Functions. https://arxiv.org/abs/1602.00013

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