# 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} }

. 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…

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