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Algebro-geometric solutions of the Baxter-Szegő difference equation. (English) Zbl 1080.37075
Summary: We derive theta function representations of algebro-geometric solutions of a discrete system governed by a transfer matrix associated with (an extension of) the trigonometric moment problem studied by G. Szegő and G. Baxter. We also derive a new hierarchy of coupled nonlinear difference equations satisfied by these algebro-geometric solutions.

MSC:
37K20 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions
33E05 Elliptic functions and integrals
39A10 Additive difference equations
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