The Cauchy-Problem for fundamental solutions of formally self-adjoint wave operators on globally hyperbolic Lorentzian manifolds

20.04.2017, 16:15 Uhr  –  Haus 9, Raum 0.14
Forschungsseminar Differentialgeometrie

Max Lewandowski

We start by discussing under which circumstances a fundamental solution can be restricted to a spacelike Cauchy hypersurface so that the corresponding Cauchy problem is well-posed which will demand some basic microlocal analysis. For the resulting solution we can derive Green's operators and, assuming the wave operator to be formally self-adjoint, prove certain properties of the fundamental solution.