• Corpus ID: 250264556

Resonances near spectral thresholds for multichannel discrete Schr\"odinger operators

@inproceedings{Assal2022ResonancesNS,
  title={Resonances near spectral thresholds for multichannel discrete Schr\"odinger operators},
  author={Marouane Assal and O. Bourget and Pablo Miranda and Diomba Sambou},
  year={2022}
}

• M. Assal, O. Bourget, +1 author D. Sambou
• Published 2 March 2022
• Mathematics

. We study the distribution of resonances of discrete Hamiltonians of the form H 0 + V , near the thresholds of the spectrum of H 0 . Here, the unperturbed operator H 0 is a multichannel Laplace type operator on (cid:96) 2 ( Z ) ⊗ G where G is an abstract separable Hilbert space, and V is a suitable compact perturbation. We distinguish two cases. If G is of finite dimension, resonances exist and do not accumulate at the thresholds in the spectrum of H 0 . We compute exactly their number and give a precise description on their location in clusters around some special points in the complex plane. If G is of infinite dimension, an accumulation phenomenon occurs at some thresholds. We describe it by means of an asymptotical analysis of the counting function of resonances. Consequences on the distribution of the complex eigenvalues are also given.