Wave front sets of different regularity

31.01.2022, 16:15  –  2.09.0.12
Forschungsseminar Differentialgeometrie

Rubens Longhi

The usual notion of wavefront set identifies the directions along which a distribution \(u\) fails to be smooth. We present an equivalent definition that makes use of the Radon transform and which is suitable for a refinement of the notion of wavefront set. The aim is to define \(\mathcal{WF_F}\)identifying the directions along which \(u \) fails to have a certain regularity \(\mathcal{F}\), for example Sobolev regularity \(H^s\) and possibly extend the theorems about the propagation of singularities to this setting.