Resonance projectors and asymptotics for 𝑟-normally hyperbolic trapped sets

Dyatlov, Semyon ^{1 ,  2}

¹ Department of Mathematics, University of California, Berkeley, California 94720
² Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

Journal of the American Mathematical Society, Tome 28 (2015) no. 2, pp. 311-381

Résumé

We prove a Weyl law for 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 are motivated by wave dynamics for black holes. The key step is a construction of a Fourier integral operator which microlocally projects onto the resonant states. In addition to the Weyl law, this operator provides new information about microlocal properties of resonant states.

Détail

DOI : 10.1090/S0894-0347-2014-00822-5

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