Geodesic
Essential Spectrum of Difference Operators on Periodic Metric Spaces
Funkcionalʹnyj analiz i ego priloženiâ, Tome 43 (2009) no. 2, pp. 83-87

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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.
Keywords: difference operator, discrete metric space, periodic graph, Fredholm property, essential spectrum. 
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     author = {V. S. Rabinovich and S. Roch},
     title = {Essential {Spectrum} of {Difference} {Operators} on {Periodic} {Metric} {Spaces}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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V. S. Rabinovich; S. Roch. Essential Spectrum of Difference Operators on Periodic Metric Spaces. Funkcionalʹnyj analiz i ego priloženiâ, Tome 43 (2009) no. 2, pp. 83-87. http://geodesic.mathdoc.fr/item/FAA_2009_43_2_a8/