Algebro-Geometric Solutions of a Discrete System Related to the   Trigonometric Moment Problem
  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 Szego and Baxter. We also derive a new hierarchy of coupled nonlinear difference equations satisfied by these algebro-geometric solutions. 
Jeffrey S. Geronimo, Fritz Gesztesy, and Helge Holden