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The matricial Schur problem in both nondegenerate and degenerate cases |
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| Authors: | Bernd Fritzsche Bernd Kirstein Andreas Lasarow |
| Institution: | 1. Mathematisches Institut, Universit?t Leipzig, Postfach 10 09 20, 04009 Leipzig, Germany;2. Phone: +49 (0)341 9732106, Fax: +49 (0)341 9732199;3. Departement Computerwetenschappen, K. U. Leuven, Celestijnenlaan 200A, B‐3001 Heverlee (Leuven), Belgium;4. Phone: +32 (0)16 327087, Fax: +32 (0)16 327996 |
| Abstract: | The principal object of this paper is to present a new approach simultaneously to both nondegenerate and degenerate cases of the matricial Schur problem. This approach is based on an analysis of the central matrixvalued Schur functions which was started in 24]–26] and then continued in 27]. In the nondegenerate situation we will see that the parametrization of the solution set obtained here coincides with the well‐known formula of D. Z. Arov and M. G. Kre?n for that case (see 1]). Furthermore, we give some characterizations of the situation that the matricial Schur problem has a unique solution (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
| Keywords: | Matricial Schur problem Arov− Kreĭ n representation of the solution set central matrix‐valued Schur functions |