Microlocal analysis of Colombeau's generalized functions on a manifold

Abstract

Various approaches to the space of Colombeau's generalized functions script G sign(X) on a C∞-manifold X are analyzed. The wave front set of G ∈ script G sign(X) is defined. The estimate of the wave front set for fxG, where f : X → Y is a C∞ -mapping and G ∈ script G sign(Y), is given. The restriction on a submanifold is determined.