On the Largest Minorants Associated with a Matrix-Valued Caratheodory Function and Spectral Factorization

Abstract

We will study various aspects of largest minorants associated with matrix-valued Carathéodory functions in the context of spectral factorization. The first main aim is to derive explicit interrelations between the largest minorants associated with a Cayley-linked pair consisting of a matrtxvalued Carathéodory function and a matrix-valued Schur function. The second goal is to derive corresponding factorizaions for the normalized limit semi-radius functions associated with a matrix-valued Carathéodory function having finite entropy.