Communications in Mathematical Physics

, Volume 258, Issue 1, pp 149–177

Algebro-Geometric Solutions of the Baxter–Szegő Difference Equation

  • Jeffrey S. Geronimo
  • Fritz Gesztesy
  • Helge Holden

DOI: 10.1007/s00220-005-1305-x

Cite this article as:
Geronimo, J., Gesztesy, F. & Holden, H. Commun. Math. Phys. (2005) 258: 149. doi:10.1007/s00220-005-1305-x


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 Szegő and Baxter. We also derive a new hierarchy of coupled nonlinear difference equations satisfied by these algebro-geometric solutions.

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Jeffrey S. Geronimo
    • 1
  • Fritz Gesztesy
    • 2
  • Helge Holden
    • 3
  1. 1.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Department of MathematicsUniversity of MissouriColumbiaUSA
  3. 3.Department of Mathematical SciencesNorwegian University of Science and TechnologyTrondheimNorway