Clusters of Resonances for a Non-Self Adjoint Multichannel Discrete Schrödinger Operator

We study the distribution of resonances for discrete Hamiltonians of the form H<inf>0</inf> + V near the thresholds of the spectrum of H<inf>0</inf>. Here, the unperturbed operator H<inf>0</inf> is a multichannel Laplace type operator on ℓ<inf>2</inf>(Z; C<inf>N</inf> )≅ℓ<inf>2</inf>(Z) ⊗ C<inf>N</inf> and V is a non-selfadjoint compact perturbation. We compute the exact number of resonances and give a precise description on their location in clusters around some special points in the complex plane. © 2025 Author(s).