A complete classification of threshold properties for one-dimensional discrete Schrödinger operators

Kenichi Ito, Arne Jensen

We consider the discrete one-dimensional Schrödinger operator $H=H_0+V$, where $(H_{0}x)[n]=-(x[n+1]+x[n-1]-2x[n])$ and $V$ is a self-adjoint operator on ${\ell }^2(\mathbb{Z})$ with a…