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On the characterization and parametrization of minimal spectral factors. (English) Zbl 0848.30023

Let \(\Phi\) be a coercive spectral function. The author shows the existence of an essentially, unique, stable, minimum (maximum) for \(\Phi\). The phase function \(T_0\) corresponding to \(\Phi\) is defined by \(T_0= \overline W^{- 1}_+ W_0\), where \(W_-\) and \(\overline W_+\) are the stable, minimum phase spectral factors respectively. He gives a characterization of minimal spectral factors in terms of minimal factorizations of the phase function. A minimal spectral factor is completely determined by primal and dual Lindquist-Picci pairs that are completely determined by factorizations of the inner functions. The factorizations of inner functions are completely determined by solutions of associated Riccati equations. Then he gives the parametrization of the set of minimal spectral factors in terms of state space formulas using two solutions of Riccati equations.
Reviewer: T.Nakazi (Sapporo)

MSC:

30D50 Blaschke products, etc. (MSC2000)
47A68 Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators
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