92-172 Krishna M.

Absolutely continuous spectrum for sparce Potentials (18K, AmsTeX) Oct 30, 92

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Abstract. In this paper we show that bounded perturbation of the discrete laplacian with a potential that is sparcely supported ( a notion made precise in the paper ) produces absolutely continuous spectrum in the interval [-2$\nu$, 2$\nu$] for large dimension $\nu$. We note that the potential need not give rise to a compact operator, let alone have decay at infinity.

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