From quasimodes to resonances: exponentially decaying perturbations

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.

References in corpus (2)

• On quasinormal modes of asymptotically anti-de Sitter black holes
• Quasi-normal modes and exponential energy decay for the Kerr-de Sitter black hole

Cited by in corpus (5)

• Characterization of edge states in perturbed honeycomb structures
• Mathematical Study of Scattering Resonances
• Resonances as Viscosity Limits for Exponentially Decaying Potentials
• Non-linear instability of slowly rotating Kerr-AdS black holes
• Effective upper bounds on the number of resonance in potential scattering