Algebro-Geometric Solutions of a Discrete System Related to the Trigonometric Moment Problem

TL;DR

This paper develops theta function representations for solutions of a discrete system linked to the trigonometric moment problem, introducing a new hierarchy of nonlinear difference equations.

Contribution

It provides novel algebro-geometric solutions and a hierarchy of coupled nonlinear difference equations for the discrete system related to the trigonometric moment problem.

Findings

Theta function representations of solutions derived

New hierarchy of coupled nonlinear difference equations established

Extension of the trigonometric moment problem studied

Abstract

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.