article · Pacific Journal of Mathematics · 2015

From quasimodes to resonances: exponentially decaying perturbations

Cited by 11Open access

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.

Cite this paper

APA 7

Gannot, O. (2015). From quasimodes to resonances: exponentially decaying perturbations. Pacific Journal of Mathematics, 277(1), 77–97. https://doi.org/10.2140/pjm.2015.277.77

MLA 9

Gannot, Oran. “From quasimodes to resonances: exponentially decaying perturbations.” Pacific Journal of Mathematics, vol. 277, no. 1, 2015, pp. 77–97, https://doi.org/10.2140/pjm.2015.277.77.

Chicago

Gannot, Oran. 2015. “From quasimodes to resonances: exponentially decaying perturbations.” Pacific Journal of Mathematics 277 (1): 77–97. https://doi.org/10.2140/pjm.2015.277.77.

Harvard

Gannot, O. (2015) ‘From quasimodes to resonances: exponentially decaying perturbations’, Pacific Journal of Mathematics, 277(1), pp. 77–97. Available at: https://doi.org/10.2140/pjm.2015.277.77.

BibTeX

@article{gannot2015quasimodes,
  title = {{From quasimodes to resonances: exponentially decaying perturbations}},
  author = {Gannot, Oran},
  journal = {Pacific Journal of Mathematics},
  volume = {277},
  number = {1},
  pages = {77--97},
  year = {2015},
  doi = {10.2140/pjm.2015.277.77}
}

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