Microlocal analysis in generalized function algebras based on generalized points and generalized directions

We develop a refined theory of microlocal analysis in the algebra G(Ω) of Colombeau generalized functions. In our approach, the wave front is a set of generalized points in the cotangent bundle of Ω, whereas in the theory developed so far, it is a set of nongeneralized points. We also show consistency between both approaches.

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