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arXiv · 2410.08679

The Hahn-Banach theorem in spaces of nonlinear generalized functions

Djamel eddine Kebiche·Paolo Giordano
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Abstract

In this paper, we establish a suitable version of the Hahn-Banach theorem within the framework of Colombeau spaces, a class of spaces used to model generalized functions. Our approach addresses the case where maps are defined $\varepsilon$-wise, which simplifies the framework and makes the extension of linear functionals more manageable. As an application of our main result, we demonstrate the separation of convex sets in Colombeau spaces.

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Djamel eddine Kebiche, Paolo Giordano. 2024-10-11. The Hahn-Banach theorem in spaces of nonlinear generalized functions. https://arxiv.org/abs/2410.08679

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