Abstract.
Let (X, ~) be a combinatorial graph the vertex set X of which is a discrete metric space. We suppose that a discrete group G acts freely on (X, ~) and that the fundamental domain with respect to the action of G contains only a finite set of points. A graph with these properties is called periodic with respect to the group G. We examine the Fredholm property and the essential spectrum of band-dominated operators acting on the spaces l p(X) or c_0(X), where (X, ~) is a periodic graph. Our approach is based on the thorough use of band-dominated operators. It generalizes the necessary and sufficient results obtained in [39] in the special case \(X = G = {\mathbb{Z}}^{n}\) and in [42] in case X = G is a general finitely generated discrete group.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Additional information
Dedicated to the memory of Georgii Semenovich Litvinchuk
Submitted: May 21, 2007. Revised: September 25, 2007. Accepted: November 5, 2007.
Rights and permissions
About this article
Cite this article
Rabinovich, V.S., Roch, S. Fredholm Properties of Band-dominated Operators on Periodic Discrete Structures. Complex anal.oper. theory 2, 637–668 (2008). https://doi.org/10.1007/s11785-008-0071-0
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11785-008-0071-0