Monatshefte für Mathematik

, Volume 181, Issue 1, pp 205–215 | Cite as

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

  • Hans Vernaeve


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


Algebras of generalized functions Microlocal analysis 

Mathematics Subject Classification

46F30 35A27 35D10 


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Copyright information

© Springer-Verlag Wien 2015

Authors and Affiliations

  1. 1.Ghent UniversityGentBelgium

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