Integration and Microlocal Analysis in Colombeau Algebras of Generalized Functions

We study integration and Fourier transform in the Colombeau algebra G of t tempered generalized functions using a general damping factor. This unifies different settings described earlier by J. F. Colombeau, M. Nedeljikov, S. Pilipovi´c, 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 S X inside G . Finally we investigate the notion of wave front set in the t Colombeau algebra G V., V an open subset of Rn, and show that it is in fact independent of the damping measure used for Fourier transform