From quasimodes to resonances: Exponentially decaying perturbations

Oran Gannot*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)77-97
Number of pages21
JournalPacific Journal of Mathematics
Issue number1
StatePublished - 2015


  • Exponentially decaying potentials
  • Quasimodes
  • Scattering resonances

ASJC Scopus subject areas

  • General Mathematics


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