期刊
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
卷 354, 期 3, 页码 1215-1231出版社
AMER MATHEMATICAL SOC
DOI: 10.1090/S0002-9947-01-02906-3
关键词
scattering resonances; hyperbolic manifolds
类别
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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