Restriction Bounds for the Free Resolvent and Resonances in Lossy Scattering
نویسنده
چکیده
We establish high energy L estimates for the restriction of the free Green’s function to hypersurfaces in R, d ≥ 1. As an application, we estimate the size of a logarithmic resonance free region for scattering by potentials of the form V ⊗ δΓ, where Γ ⊂ R 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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