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ISSN 1088-6850(e) ISSN 0002-9947(p)

Scattering poles for asymptotically hyperbolic manifolds

Author(s): David Borthwick; Peter Perry
Journal: Trans. Amer. Math. Soc. 354 (2002), 1215-1231.
MSC (2000): Primary 58J50, 35P25; Secondary 47A40
Posted: October 26, 2001
MathSciNet review: 1867379
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Abstract: For a class of manifolds that includes quotients of real hyperbolic -dimensional space by a convex co-compact discrete group, we show that the resonances of the meromorphically continued resolvent kernel for the Laplacian on coincide, with multiplicities, with the poles of the meromorphically continued scattering operator for . 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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