Journal
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume 354, Issue 3, Pages 1215-1231Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/S0002-9947-01-02906-3
Keywords
scattering resonances; hyperbolic manifolds
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For a class of manifolds X that includes quotients of real hyperbolic (n + 1)-dimensional space by a convex co-compact discrete group, we show that the resonances of the meromorphically continued resolvent kernel for the Laplacian on X coincide, with multiplicities, with the poles of the meromorphically continued scattering operator for X. In order to carry out the proof, we use Shmuel Agmon's perturbation theory of resonances to show that both resolvent resonances and scattering poles are simple for generic potential perturbations.
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