Galkowski, J;
Smith, HF;
(2015)
Restriction Bounds for the Free Resolvent and Resonances in Lossy Scattering.
International Mathematics Research Notices
, 2015
(16)
pp. 7473-7509.
10.1093/imrn/rnu179.
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Abstract
We establish high energy L2 estimates for the restriction of the free Green's function to hypersurfaces in Rd, 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⊂Rd 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.
| Type: | Article |
|---|---|
| Title: | Restriction Bounds for the Free Resolvent and Resonances in Lossy Scattering |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1093/imrn/rnu179 |
| Publisher version: | https://doi.org/10.1093/imrn/rnu179 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10083915 |
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