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<p>The solution set of the matricial Schur problem is represented in both non-degenerate and degenerate cases by a certain linear fractional transformation. The special aspect here is that the matrix polynomials occurring there are explicitly constructed from the given data and that connections with certain systems of orthogonal matrix polynomials are shown. As a byproduct, the possibility of explicitly representing central Schur functions as rational matrix functions arises.</p>

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Orthogonal Matrix Polynomials Connected with the Matricial Schur Problem

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月5日

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  • Vladimir K. Dubovoy,
  • Bernd Fritzsche,
  • Bernd Kirstein,
  • Conrad Mädler

摘要

The solution set of the matricial Schur problem is represented in both non-degenerate and degenerate cases by a certain linear fractional transformation. The special aspect here is that the matrix polynomials occurring there are explicitly constructed from the given data and that connections with certain systems of orthogonal matrix polynomials are shown. As a byproduct, the possibility of explicitly representing central Schur functions as rational matrix functions arises.