Construction of Isozaki-Kitada modifiers for discrete Schrödinger operators on general lattices

Abstract

We consider a scattering theory for convolution operators on $\mathcal{H}={\ell }^2({\mathbb{Z}}^d;{\mathbb{C}}^n)$ perturbed with a long-range potential $V:{\mathbb{Z}}^d\to {\mathbb{R}}^n$. One of the motivating examples is discrete Schrödinger operators on ${\mathbb{Z}}^d$-periodic graphs. We construct time-independent modifiers, so-called Isozaki-Kitada modifiers, and we prove that the modified wave operators with the above-mentioned Isozaki-Kitada modifiers exist and that they are complete.

arXiv comment21 pages