On the foundations of nonlinear generalized functions I

Details On the foundations of nonlinear generalized functions I On the foundations of nonlinear generalized functions I

1999-12-28

arxiv.org/abs/math/9912214v1

Mem. Amer. Math. Soc. 153, No. 729, 2001.

Mathematics

Functional Analysis

60 pages, LaTeX

Scientific paper

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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