06-56 M. Mantoiu, S. Richard, R. Tiedra de Aldecoa

Spectral analysis for adjacency operators on graphs (375K, postscript) Mar 7, 06

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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.

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