Essential Spectrum of Difference Operators on Periodic Metric Spaces

The paper deals with the study of Fredholm property and essential spectrum of general difference (or band) operators acting on the spaces $l^{p}(X)$ on a discrete metric space $X$ periodic with respect to the action of a finitely generated discrete group. The Schrödinger operator on a combinatorial periodic graph is a prominent example of a band operator of this kind.