Integration and microlocal analysis in Colombeau algebras of generalized functions

We study integration and Fourier transform in the Colombeau algebra G(T) of tempered generalized functions using a general damping factor. This unifies different settings described earlier by J. F. Colombeau, M. Nedeljikov, S. Pilipovic, and M. Damsma (for a simplified version). Further we prove characterizations of regularity for generalized functions in two situations: compactly supported or in the image of T' inside G(T). Finally we investigate the notion of wave front set in the Colombeau algebra G(Omega), Omega an open subset of R-n, and show that it is in fact independent of the damping measure used for Fourier transform. (C) 1999 Academic Press.