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arXiv · 1401.6243

Restriction Bounds for the Free Resolvent and Resonances in Lossy Scattering

Jeffrey Galkowski·Hart Smith
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Abstract

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.

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Jeffrey Galkowski, Hart Smith. 2014-01-24. Restriction Bounds for the Free Resolvent and Resonances in Lossy Scattering. https://doi.org/10.1093/imrn/rnu179

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