ON A HARDY SPACE APPROACH TO THE ANALYSIS OF SPECTRAL FACTORS

The paper presents a study of several problems related to spectral fac torizations. We assume only a very weak form of coercivity for the p x p spectral function Phi and look at the set W-m of all rectangular, p x m spectral factors. The main object is the arithmetization of the g eometry of the set of minimal, stable spectral factors by employing Ha rdy space techniques and the arithmetic of inner functions. Particular attention is paid to the study of various partial orders associated w ith the set of spectral factors.