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

TL;DR

This paper investigates the mathematical properties of wave operators on Lorentzian scattering spaces, establishing essential self-adjointness and the limiting absorption principle using a Fredholm framework.

Contribution

It introduces a novel approach to prove self-adjointness and the limiting absorption principle for wave operators in generalized Lorentzian scattering settings.

Findings

Established essential self-adjointness of wave operators.

Proved the limiting absorption principle in Lorentzian scattering spaces.

Developed a Fredholm framework for spectral analysis.

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 its dense range in L^2 when acting on an appropriate subdomain.