Essential self-adjointness of the wave operator and the limiting absorption principle on Lorentzian scattering spaces

Abstract

We discuss the essential self-adjointness of wave operators, as well as the limiting absorption principle, in generalizations of asymptotically Minkowski settings. This is obtained via using a Fredholm framework for inverting the spectral family first, and then refining its conclusions to show dense range of $\square -\lambda$, $\lambda \notin \mathbb{R}$, in $L_{\mathrm{sc}}^2$ when acting on an appropriate subdomain.