Microlocalisation on a manifold with boundary-II

16.11.2023, 16:00  –  Haus 9, Raum 0.14
Forschungsseminar Differentialgeometrie

Onirban Islam

Loosely speaking, if two (pseudo)differential operators differ only by smoothing operators then they are called microlocal conjugate to each other. It is a classic result by Duistermaat and Hörmander that scalar pseudodifferential operators of real-principal type on a boundaryless manifold can be always microlocalised to the partial derivative. On a manifold with boundary, an analogue of this result is due to Melrose for scalar b-pseudodifferential operators. In this talk, I shall explain these notions, in particular, the generalisation in the bundle setting. Then, I shall sketch how to incorporate boundary conditions using the so-called third Green's identity and single-layer potential.