Wiener algebra of operators on the lattice (μ ℤ)ⁿ depending on the small parameter μ>0: An International Journal

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 (μℤ)ⁿ = {x∈ℝⁿ: x = μy,y∈ℤⁿ} for small μ>0. We consider the discrete Schrödinger operators on (μℤ)ⁿ as applications and study the relation between the spectra of Schrödinger operators on ℝⁿ and its discrete models on (μℤ)ⁿ for small μ>0.