Abstract
Let (X, ρ) be a discrete metric space. We suppose that the group acts freely on X and that the number of orbits of X with respect to this action is finite. Then we call X a -periodic discrete metric space. We examine the Fredholm property and essential spectra of band-dominated operators on lp(X) when 1 < p < ∞. Our approach is based on the theory of band-dominated operators on and their limit operators. In the case where X is the set of vertices of a combinatorial graph, the graph structure defines a Schrödinger operator on lp(X) in a natural way. We illustrate our approach by determining the essential spectra of Schrödinger operators with slowly oscillating potential both on zig-zag and on hexagonal graphs, the latter being related to nano-structures.
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