Fundamental solutions of partial derivatives on a half-space
– Raum 1.10
The Dirac operator on a globally hyperbolic spacetime admits unique retarded and advanced fundamental solutions. They are well-known to be Lagrangian distributions. Recently, Bär and Gehring (arXiv:2210.15052 [math.DG]) have proven the existence and uniqueness of such fundamental solutions for a Dirac operator with non-local boundary conditions on a globally hyperbolic spin-spacetime with timelike boundary. In this talk, I shall sketch how the Lagrangian distributional description of these fundamental solutions can be obtained. As a preparation, the fundamental solutions of a partial derivative on a d-dimensional half-space will be discussed.