On the foundations of nonlinear generalized functions I

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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.
60 pages, LaTeX

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Functional Analysis, Mathematical Physics, 46F30; 26E15; 46E50; 35D05

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http://salesiana.dossiersoluciones.com/handle/123456789/79681

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9912214
 http://arxiv.org/abs/math/9912214
 Mem. Amer. Math. Soc. 153, No. 729, 2001.

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arXiv