The functional analytic foundation of Colombeau algebras
arXiv:1305.1460
Abstract
Colombeau algebras constitute a convenient framework for performing nonlinear operations like multiplication on Schwartz distributions. Many variants and modifications of these algebras exist for various applications. We present a functional analytic approach placing these algebras in a unifying hierarchy, which clarifies their structural properties as well as their relation to each other.
31 pages; updated section on sheaf properties