English

On the foundations of nonlinear generalized functions I

Functional Analysis 2007-05-23 v1 Mathematical Physics math.MP

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.

Keywords

Cite

@article{arxiv.math/9912214,
  title  = {On the foundations of nonlinear generalized functions I},
  author = {Eva Farkas and Michael Grosser and Michael Kunzinger and Roland Steinbauer},
  journal= {arXiv preprint arXiv:math/9912214},
  year   = {2007}
}

Comments

60 pages, LaTeX

R2 v1 2026-07-22T18:06:01.116Z