Wave front set

Summary

The wave front set of a distribution records where the distribution fails to be smooth, and in which frequency directions it fails. It is a closed subset of $\Omega \times (\R^n \setminus \set{0})$ that is conic in the second variable. Its projection to $\Omega$ is the singular support, the set of points near which the distribution is not a smooth function. It is the basic object of microlocal analysis and the language of propagation of singularities. See the definition.