Microlocal analysis in the dual of a Colombeau algebra: generalized wave front sets and noncharacteristic regularity

We introduce different notions of wave front set for the functionals in the dual of the Colomboau algebra script G signc(Ω) providing a way to measure the script G sign and the script G sign∞ - regularity in ℒ(script G signc(Ω),ℂ̃). For the smaller family of functional having a "basic structure" we obtain a Fourier transform-characterization for this type of generalized wave front sots and results of noncharacteristic script G sign and script G sign ∞-regularity.