Factorization of a class of 2 x 2 matrix symbols by reduction to a scalar factorization

摘要

Using the reduction of a vector Riemann-Hilbert problem on the unit circle to a scalar problem on a contour in a Riemann surface, a factorization method for a class of symbols is described. The class of symbols involves outer functions and rational functions of the square root of a quotient of first degree polynomials. An application to a problem in the field of integrable systems of infinite dimension is presented.