English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

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 unperturbedoperator $H_0$ is a multichannel Laplace type operator on $\ell^2(\mathbb Z;\mathfrak{G}) \cong \ell^2(\mathbb Z)\otimes \mathfrak{G}$ where ${\mathfrakG}$ is an abstract separable Hilbert space, and $V$ is a suitablenon-selfadjoint compact perturbation. We distinguish two cases. If ${\mathfrakG}$ is of finite dimension, we prove that resonances exist and do notaccumulate at the thresholds in the spectrum of $H_0$. Furthermore, we computeexactly their number and give a precise description on their location inclusters in the complex plane. If ${\mathfrak G}$ is of infinite dimension, anaccumulation phenomenon occurs at some thresholds. We describe it by means ofan asymptotical analysis of the counting function of resonances. Consequenceson the distribution of the complex and the embedded eigenvalues are also given.

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