Open Collections

A groupoid approach to pseudodifferential operators

Banff International Research Station for Mathematical Innovation and Discovery

The tangent groupoid is a geometric device for glueing a pseudodifferential operator to its principal symbol, via a deformation family. We will discuss a converse to this: briefly, pseudodifferential kernels are precisely those distributions that extend to distributions on the tangent groupoid that are essentially homogeneous with respect to the natural $R^+$-action. One could see this as a simple new definition of a classical pseudodifferential operator. Moreover, we will show that, armed with an appropriate generalization of the tangent groupoid, this approach allows us to easily construct more exotic pseudodifferential calculi, such as the Heisenberg calculus. (Joint work with Erik van Erp.)

Mathematics; Differential geometry; Topological groups, lie groups

video/mp4

Author affiliation: Univesité Clermont Auvergne

2017-10-18

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/63336

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/