11-161 V. Bach, W. de Siqueira Pedra, and S. N. Lakaev

Bounds on the Pure Point Spectrum of Lattice Schr dinger Operators (269K, pdf) Oct 18, 11

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Abstract. In dimension d≥3 a variational principle for the size of the pure point spectrum, thus taking embedded eigenvalues into account, of Schr dinger operators H(e,V) on the lattice is proven. The dispersion relations e are assumed to be Morse functions and the potentials V(x) to decay faster than |x|^{−2(d+3)}, but are not necessarily of definite sign. The proof is based on resolvent estimates for H(e,V′), for small V′, combined with positivity arguments.

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