Topological Structures in Colombeau Algebras: Investigation of the Duals of ${\cal G}_{{\rm c}}(\Omega)$ , ${\cal G}(\Omega)$ and ${\cal G}_{{\cal S}}({\Bbb R}^n)$

Abstract

We study the topological duals of the Colombeau algebras \({\cal G}_{{\rm c}}(\Omega)\), \({\cal G}(\Omega)\) and \({\cal G}_{{\cal S}}({\Bbb R}^n)\), discussing some continuous embeddings and the properties of generalized delta functionals.