Scattering on stratified media: the micro-local properties of the scattering matrix and recovering asymptotics of perturbations

Resolvent Trace Asymptotics on Stratified Spaces

Let $(M,g)$ be a compact smoothly stratified pseudomanifold with an iterated cone-edge metric satisfying a spectral Witt condition. Under these assumptions the Hodge-Laplacian $Δ$ is essentially self-adjoint. We establish the asymptotic expansion for the resolvent trace of $Δ$. Our method proceeds by induction on the depth and applies in principle to a larger class of second-order differential operators of regular-singular type, e.g., Dirac Laplacians. Our arguments are functional analytic, do not rely on microlocal techniques and are very explicit. The results of this paper provide a basis fo…