The green function of the discrete finite-gap one-energy two-dimensional Schrödinger operator on the quad graph

Abstract

The finite-gap approach to constructing the discrete Schrodinger operator on a quad graph expressed as a two-dimensional integer sublattice in d-dimensional space is used. The Green function for this operator is explicitly expressed as an integral over special contours of the differential constructed from spectral data. The resulting function has a well-known asymptotics.