07-206 Elke Rosenberger, Markus Klein

Agmon-Type estimates for a class of difference operators (458K, pdf) Sep 10, 07

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Abstract. We analyze a general class of difference operators H_epsilon = T_epsilon + V_epsilon on l^2(epsilon Z^d), where V_epsilon is a one-well potential and epsilon is a small parameter. We construct a Finslerian distance d induced by H_epsilon and show that short integral curves are geodesics. Then we show that Dirichlet eigenfunctions decay exponentially with a rate controlled by the Finsler distance to the well. This is analog to semiclassical Agmon estimates for Schr dinger operators.

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