Scattering poles for asymptotically hyperbolic manifolds

Borthwick, David; Perry, Peter

doi:10.1090/S0002-9947-01-02906-3

Scattering poles for asymptotically hyperbolic manifolds
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by David Borthwick and Peter Perry PDF

Trans. Amer. Math. Soc. 354 (2002), 1215-1231 Request permission

Abstract:

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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