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Scattering poles for asymptotically hyperbolic manifolds. (English) Zbl 1009.58021

The authors 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 \(X\), for a class of manifolds \(X\) that includes quotients of real hyperbolic \((n + 1)\)-dimensional space by a convex co-compact discrete group. In order to carry out the proof, they use Shmuel Agmon’s perturbation theory of resonances to show that both resolvent resonances and scattering poles are simple for generic potential perturbations.

MSC:

58J50 Spectral problems; spectral geometry; scattering theory on manifolds
35P25 Scattering theory for PDEs
47A40 Scattering theory of linear operators
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