2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72117We 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 Szego and Baxter. We also derive a new hierarchy of coupled nonlinear difference equations satisfied by these algebro-geometric solutions.22 pagesSpectral TheoryMathematical Physics35Q53; 58F07; 35Q51text