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Abstract: The main aim of the paper is the investigation of a relation between the essential spectrum and the exponential decay at infinity of eigenfunctions of the lattice analogs of Schrödinger and Dirac operators.

The aim of the paper is to present some results concerning pseudodifference operators on ℤN, which are a discrete analog of standard pseudodifferential operators on ℝN. We study the Fredholm property of pseudodifference operators acting in weighted lp spaces on ℤN and the Phragmen-Lindelöf principle for solutions of pseudodifference equations and give applications of these results to discrete Schrö dinger operators on ℤN.