Journal
PACIFIC JOURNAL OF MATHEMATICS
Volume 277, Issue 1, Pages 77-97Publisher
PACIFIC JOURNAL MATHEMATICS
DOI: 10.2140/pjm.2015.277.77
Keywords
scattering resonances; quasimodes; exponentially decaying potentials
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We consider self-adjoint operators of black-box type which are exponentially close to the free Laplacian near infinity, and prove an exponential bound for the resolvent in a strip away from resonances. Here the resonances are defined as poles of the meromorphic continuation of the resolvent between appropriate exponentially weighted spaces. We then use a local version of the maximum principle to prove that any cluster of real quasimodes generates at least as many resonances, with multiplicity, rapidly converging to the quasimodes.
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