Resonances under Rank One Perturbations
Spectral Theory
2017-10-11 v1
Abstract
We study resonances generated by rank one perturbations of selfadjoint operators with eigenvalues embedded in the continuous spectrum. Instability of these eigenvalues is analyzed and almost exponential decay for the associated resonant states is exhibited. We show how these results can be applied to Sturm-Liouville operators. Main tools are the Aronszajn-Donoghue theory for rank one perturbations, a reduction process of the resolvent based on Feshbach-Livsic formula, the Fermi golden rule and a careful analysis of the Fourier transform of quasi-Lorentzian functions. We relate these results to sojourn time estimates and spectral concentration phenomena
Keywords
Cite
@article{arxiv.1707.01597,
title = {Resonances under Rank One Perturbations},
author = {Olivier Bourget and Victor Cortes and Rafael del Rio and Claudio Fernandez},
journal= {arXiv preprint arXiv:1707.01597},
year = {2017}
}