From quasimodes to resonances: exponentially decaying perturbations
Analysis of PDEs
2016-01-20 v3 Spectral Theory
Abstract
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.
Keywords
Cite
@article{arxiv.1305.2896,
title = {From quasimodes to resonances: exponentially decaying perturbations},
author = {Oran Gannot},
journal= {arXiv preprint arXiv:1305.2896},
year = {2016}
}