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On the foundations of nonlinear generalized functions I

Eva Farkas·Michael Grosser·Michael Kunzinger·Roland Steinbauer
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Abstract

We construct a diffeomorphism invariant (Colombeau-type) differential algebra canonically containing the space of distributions in the sense of L. Schwartz. Employing differential calculus in infinite dimensional (convenient) vector spaces, previous attempts in this direction are unified and completed. Several classification results are achieved and applications to nonlinear differential equations involving singularities are given.

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Eva Farkas, Michael Grosser, Michael Kunzinger, Roland Steinbauer. 1999-12-28. On the foundations of nonlinear generalized functions I. https://arxiv.org/abs/math/9912214

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