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Zeitschrift für Analysis und ihre Anwendungen


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Volume 12, Issue 3, 1993, pp. 471–490
DOI: 10.4171/ZAA/552

Published online: 1993-09-30

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

B. Fritzsche[1] and B. Kirstein[2]

(1) Universität Leipzig, Germany
(2) Universität Leipzig, Germany

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.

Keywords: Carathéodory functions, largest rninorants, Weyl matrix balls

Fritzsche B., Kirstein B.: On the Largest Minorants Associated with a Matrix-Valued Caratheodory Function and Spectral Factorization. Z. Anal. Anwend. 12 (1993), 471-490. doi: 10.4171/ZAA/552