  Szego's procedure to connect orthogonal polynomials on the unit circle and
orthogonal polynomials on [-1,1] is generalized to nonsymmetric measures. It
generates the so-called semi-orthogonal functions on the linear space of
Laurent polynomials L, and leads to a new orthogonality structure in the module
LxL. This structure can be interpreted in terms of a 2x2 matrix measure on
[-1,1], and semi-orthogonal functions provide the corresponding sequence of
orthogonal matrix polynomials. This gives a connection between orthogonal
polynomials on the unit circle and certain classes of matrix orthogonal
polynomials on [-1,1]. As an application, the strong asymptotics of these
matrix orthogonal polynomials is derived, obtaining an explicit expression for
the corresponding Szego's matrix function.
