  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.
