On the foundations of nonlinear generalized functions I and II - Grosser, Michael (Memoirs of the American Mathematical Society, 2001)
Part 1. On the Foundations of Nonlinear Generalized Functions I: Introduction Notation and terminology Scheme of construction Calculus C- and J-formalism Calculus on $U_ε(Ω)$ Construction of a diffeomorphism invariant Colombeau algebra Sheaf properties Separating the basic definition from testing Characterization results Differential equations Part 2. On the Foundations of Nonlinear Generalized Functions II: Introduction to Part 2 A simple condition equivalent to negligibility Some more calculus Non-injectivity of the canonical homomorphism from ${\mathcal G}^d(Ω)$ into ${\mathcal G}^e(Ω)$ Classification of smooth Colombeau algebras between ${\mathcal G}^d(Ω)$ and ${\mathcal G}^e(Ω)$ The algebra ${\mathcal G}^2$; classification results Concluding remarks Acknowledgments Bibliography.