Finite-gap difference opeators with elliptic coefficients and their spectral curves
A. Zabrodin
Abstract
We review recent results on the finite-gap properties of difference operators with elliptic coefficients and give explicit characterization of spectral curves for difference analogues of the higher Lamé operators. This curve parametrizes double-Bloch solutions to the difference Lamé equation. The curve depends on a positive integer number , related to its genus g by g=2, and two continuous parameters: the lattice spacing ηand the modular parameter τ. Isospectral deformations of the difference Lamé operator under Volterra flows are also discussed.
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