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On Rank Invariance of Schwarz-Pick-Potapov Block Matrices of Matricial Schur Functions

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Abstract.

We derive statements on rank invariance of Schwarz-Pick-Potapov block matrices of matrix-valued Schur functions. The rank of these block matrices coincides with the rank of some block matrices built from the corresponding section matrices of Taylor coefficients. These results are applied to the discussion of a matrix version of the classical Schur-Nevanlinna algorithm.

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Authors and Affiliations

  1. Fakultät für Mathematik und Informatik, Universität Leipzig, Augustusplatz 10, 04109, Leipzig, Germany

    Bernd Fritzsche & Bernd Kirstein

  2. Max-Planck-Institut für Mathematik in den Naturwissenschaften, Niigata University, Inselstrasse 22-26, 04103, Leipzig, Germany

    Andreas Lasarow

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  1. Bernd Fritzsche
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  2. Bernd Kirstein
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  3. Andreas Lasarow
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Correspondence to Bernd Fritzsche.

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Fritzsche, B., Kirstein, B. & Lasarow, A. On Rank Invariance of Schwarz-Pick-Potapov Block Matrices of Matricial Schur Functions. Integr. equ. oper. theory 48, 305–330 (2004). https://doi.org/10.1007/s00020-002-1181-0

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  • DOI: https://doi.org/10.1007/s00020-002-1181-0

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