Algebras of generalized functions Duality theory Wave front sets
New York Journal of Mathematics
GARETTO, C., 2006. Microlocal analysis in the dual of a Colombeau algebra: generalized wave front sets and noncharacteristic regularity. New York Journal of Mathematics, 12, pp. 275 - 318.
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.
This article was published in the New York Journal of Mathematics and the definitive version is available at: http://nyjm.albany.edu/j/2006/12-18v.pdf
Supported by FWF (Austria), grant P16820-N04 and TWF (Tyrol), grant UNI-0404/305.