2013/01/31 by Semyon Dyatlov · 1 citation
Mathematics · #math.AP #math.SP
paper · pdf · doi:10.1090/s0894-0347-2014-00822-5
80 pages, 6 figures, minor changes. To appear in JAMS
arxiv created 2014/10/15 · arxiv updated 2014/12/18
We prove an asymptotic formula for the number of scattering resonances in a strip near the real axis when the trapped set is r-normally hyperbolic with r large and a pinching condition on the normal expansion rates holds. Our dynamical assumptions are stable under smooth perturbations and motivated by the setting of black holes. The key tool is a Fourier integral operator which microlocally projects onto the resonant states in the strip. In addition to Weyl law, this operator provides new information about microlocal concentration of resonant states.