Absolutely continuous spectrum for sparse potentials |
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Authors: | M Krishna |
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Affiliation: | 1. Institute of Mathematical Sciences, Taramani, 600 113, Madras, India
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Abstract: | In this paper we show that bounded perturbation of the discrete laplacian with a potential that is sparsely supported (a notion made precise in the paper) produces absolutely continuous spectrum in the interval [?2ν, 2ν] for large dimension ν. We note that the potential need not give rise to a compact operator, let alone have decay at infinity. |
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