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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Communicated by Christian Gérard.
Submitted: July 15, 2006. Accepted: January 16, 2007.
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Măntoiu, M., Richard, S. & de Aldecoa, R.T. Spectral Analysis for Adjacency Operators on Graphs. Ann. Henri Poincaré 8, 1401–1423 (2007). https://doi.org/10.1007/s00023-007-0339-3
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DOI: https://doi.org/10.1007/s00023-007-0339-3