Ablowitz-Ladik system with discrete potential. I. Extended resolvent

TL;DR

This paper investigates the Ablowitz-Ladik linear system with a binary potential, constructing its extended resolvent operator and analyzing its singularities to deepen understanding of its spectral properties.

Contribution

The paper introduces a detailed construction of the extended resolvent operator for the Ablowitz-Ladik system with discrete potential and analyzes its singularities, advancing spectral analysis methods.

Findings

Extended resolvent operator constructed for the system

Singularities of the resolvent operator analyzed in detail

Provides insights into spectral properties of the discrete potential system

Abstract

Ablowitz-Ladik linear system with range of potential equal to {0,1} is considered. The extended resolvent operator of this system is constructed and the singularities of this operator are analyzed in detail.