Wiener algebra of operators on the lattice (Z) n depending on the small parameter >0

This article is devoted to the problems of invertibility and Fredholmness of operators in the weighted Wiener algebra acting in the weighted spaces of vector-functions on the lattice (Z)(n)={x(n):x=y,yZ(n)} for small >0. We consider the discrete Schrodinger operators on (Z)(n) as applications and study the relation between the spectra of Schrodinger operators on (n) and its discrete models on (Z)(n) for small >0.