The scattering matrix for 0th order pseudodifferential operators

Jian Wang

Published 2019-09-13Version 1

We use microlocal radial estimates to prove the full limiting absorption principle for $P$, a self-adjoint 0th order pseudodifferential operator satisfying hyperbolic dynamical assumptions as of Colin de Verdi\`ere and Saint-Raymond. We define the scattering matrix for $P-\omega$ when $\omega$ is not an embedded eigenvalue of $P$ and show that the scattering matrix extends to a unitary operator on appropriate $L^2$ spaces. The operator $P$ gives microlocal model of internal waves in stratified fluids as illustrated in the paper of Colin de Verdi\`ere and Saint-Raymond.