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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Resonance projectors and asymptotics for $r$-normally hyperbolic trapped sets
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by Semyon Dyatlov PDF
J. Amer. Math. Soc. 28 (2015), 311-381 Request permission

Abstract:

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.
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Additional Information
  • Semyon Dyatlov
  • Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
  • Address at time of publication: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
  • MR Author ID: 830509
  • ORCID: 0000-0002-6594-7604
  • Email: dyatlov@math.mit.edu
  • Received by editor(s): February 21, 2013
  • Published electronically: December 16, 2014
  • © Copyright 2014 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 28 (2015), 311-381
  • MSC (2010): Primary 35B34; Secondary 35S30, 37D05, 83C57
  • DOI: https://doi.org/10.1090/S0894-0347-2014-00822-5
  • MathSciNet review: 3300697