Elke Rosenberger (Potsdam)
For a class of elliptic self-adjoint pseudo-differential operators in a discrete semi-classical setting we give asymptotic estimates for the number of eigenvalues in a fixed interval. Here we assume the related symbols to be periodic with respect to momentum. The associated operator acts on functions on a lattice scaled by a semi-classical parameter. Under the assumption that the boundaries of the spectral interval are non-critical values of the principal symbol, we show that the exact leading order term for the number of eigenvalues is given by the phase space volume of the preimage of the interval under the principal symbol.
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