Clusters of resonances for a non-selfadjoint multichannel discrete Schrödinger operator

Abstract

We study the distribution of resonances for 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 ${\ell }^2(\mathbb{Z};{\mathbb{C}}^N)\cong {\ell }^2(\mathbb{Z})\otimes {\mathbb{C}}^N$ 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.

12 pages, 1 figure