Distribution of Resonances in Scattering by Thin Barriers

The author studies high energy resonances for the operators $-\Delta_{\partial\Omega,\delta}:=-\Delta \delta_{\partial\Omega}\otimes V\quad \textrm{and}\quad -\Delta_{\partial\Omega,\delta'}:=-\Delta \delta_{\partial\Omega}'\otimes V\partial_\nu$ where $\Omega\subset{\mathbb{R}}^{d}$ is strictly convex with smooth boundary, $V:L^{2}(\partial\Omega)\to L^{2}(\partial\Omega)$ may depend on frequency, and $\delta_{\partial\Omega}$ is the surface measure on $\partial\Omega$.