Microlocal analysis of Colombeau's generalized functions: Propagation of singularities

Abstract

We introduce the notion of pointwise regularity (script G sigṅ∞) of Colombeau's generalized functions and give comparison theorems between script G sigṅ∞ regularity, script G sign∞ - and C∞-regularity. We also define the notion of a pointwise wave front set and establish a theorem concerning the effect of a linear generalized partial differential operator on such a wave front.