Galkowski, J;
(2017)
A Quantitative Vainberg Method for Black Box Scattering.
Communications in Mathematical Physics
, 349
(2)
pp. 527-549.
10.1007/s00220-016-2635-6.
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Abstract
We give a quantitative version of Vainberg’s method relating pole free regions to propagation of singularities for black box scatterers. In particular, we show that there is a logarithmic resonance free region near the real axis of size τ with polynomial bounds on the resolvent if and only if the wave propagator gains derivatives at rate τ . Next we show that if there exist singularities in the wave trace at times tending to infinity which smooth at rate τ , then there are resonances in logarithmic strips whose width is given by τ . As our main application of these results, we give sharp bounds on the size of resonance free regions in scattering on geometrically nontrapping manifolds with conic points. Moreover, these bounds are generically optimal on exteriors of nontrapping polygonal domains.
| Type: | Article |
|---|---|
| Title: | A Quantitative Vainberg Method for Black Box Scattering |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s00220-016-2635-6 |
| Publisher version: | https://doi.org/10.1007/s00220-016-2635-6 |
| 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. |
| Keywords: | Manifold, Conic Singularity, Cone Point, Geometrically Realizeable, Wave Propagator |
| 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.ucl.ac.uk/id/eprint/10083905 |
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