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Full Description
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 $\partial\Omega$.
Contents
Introduction
Preliminaries
Meromorphic continuation of the resolvent
Boundary layer operators
Dynamical resonance free regions
Existence of resonances for the Delta potential
Appendix A. Model cases
Appendix B. Semiclassical intersecting Lagrangian distributions
Appendix C. The semiclassical Melrose-Taylor parametrix
Bibliography.
