Spectral Analysis for Adjacency Operators on Graphs |
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| Authors: | Marius Măntoiu Serge Richard Rafael Tiedra de Aldecoa |
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| Affiliation: | (1) Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1–764, RO-014700 Bucharest, Romania;(2) Institut Camille Jordan, Université Claude Bernard Lyon 1, Université de Lyon, CNRS UMR 5208, 43, boulevard du 11 novembre 1918, F-69622 Villeurbanne cedex, France;(3) Département de Mathématiques, Université de Paris XI, F-91405 Orsay cedex, France |
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| Abstract: | We put into evidence graphs with adjacency operator whose singular subspace is prescribed by the kernel of an auxiliary operator. In particular, for a family of graphs called admissible, the singular continuous spectrum is absent and there is at most an eigenvalue located at the origin. Among other examples, the one-dimensional XY model of solid-state physics is covered. The proofs rely on commutators methods. Submitted: July 15, 2006. Accepted: January 16, 2007. |
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