Intrinsic definition of the Colombeau algebra of generalized functions (Q1185382)

Let \(\Omega\) be an open subset of \(\mathbb{R}^ n\). \textit{J. F. Colombeau} [Elementary introduction to new generalized functions, North-Holland Math. Stud. 113 (1985; Zbl 0584.46024)] introduced an algebra \({\mathcal G}(\Omega)\) of generalized functions on \(\Omega\) which contains the space \({\mathcal D}'(\Omega)\) of the distributions on \(\Omega\) as a vector subspace. The purpose of this paper is to organize the basic kernel of Colombeau's theory, having as starting point an intrinsic presentation of the space \({\mathcal G}(\Omega)\). The definition of the generalized functions on manifolds is also given.