Restriction Bounds for the Free Resolvent and Resonances in Lossy Scattering

Jeffrey Galkowski, Hart F. Smith
2014 International mathematics research notices  
We establish high energy $L^2$ estimates for the restriction of the free Green's function to hypersurfaces in $\mathbb{R}^d$. As an application, we estimate the size of a logarithmic resonance free region for scattering by potentials of the form $V\otimes \delta_{\Gamma}$, where $\Gamma \subset \mathbb{R}^d$ is a finite union of compact subsets of embedded hypersurfaces. In odd dimensions we prove a resonance expansion for solutions to the wave equation with such a potential.
doi:10.1093/imrn/rnu179 fatcat:kyo54xs6lrgzhbplwmssd2urq4