Inversion of Radon transform and applications to microlocal regularity

01.12.2022, 16:00  –  Raum 1.10
Forschungsseminar Differentialgeometrie

Rubens Longhi (UP)

We aim at extending the classical notion of smooth wavefront set employing the Radon transform in order to capture different degrees of lack of \(\mathcal{F}\)-regularity of a distribution \(u\) around a certain co-direction \(\xi\), e.g. for \(\mathcal{F}=\) Sobolev or Hölder spaces on \(\mathbb{R}\). In order to extend the usual smooth microlocal regularity theorem to this setting, it is technically necessary to assume that the space of regularity \(\mathcal{F}\) is invariant under the action of a certain Fourier Integral Operator of order zero, obtained by inverting the Radon transform. In the talk we will investigate whether such operator can be reduced to a pseudodifferential one, weakening the assumptions on \(\mathcal{F}\).