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arXiv · 1510.00626

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

Hans Vernaeve
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Abstract

We develop a refined theory of microlocal analysis in the algebra ${\mathcal G}(Ω)$ 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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Hans Vernaeve. 2016-01-14. Microlocal analysis in generalized function algebras based on generalized points and generalized directions. https://doi.org/10.1007/s00605-015-0831-7

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