Microlocal analysis in generalized function algebras based on generalized points and generalized directions (Q314499)

The main contribution of this paper is refinement of \(\mathcal{G}^{\infty}\)-microlocal analysis by means of the wave front set definition as a set of generalized points in the cotangent bundle of \(\Omega\). It is shown that the projection of the wave front set in the first coordinate is the \(\tilde{\mathcal{G}}^{\infty}\)-singular support. \(\mathcal{G}^{\infty}\)-microlocal regularity is characterized in terms of \(\tilde{\mathcal{G}}^{\infty}\)-microlocal regularity.