Original Paper

On matrix-valued Herglotz-Nevanlinna functions with an emphasis on particular subclasses†

  1. Bernd Fritzsche*,
  2. Bernd Kirstein*,
  3. Conrad Mädler*

Article first published online: 11 APR 2012

DOI: 10.1002/mana.201100247

Issue

Mathematische Nachrichten

Mathematische Nachrichten

Volume 285, Issue 14-15, pages 1770–1790, October 2012

Additional Information

How to Cite

Fritzsche, B., Kirstein, B. and Mädler, C. (2012), On matrix-valued Herglotz-Nevanlinna functions with an emphasis on particular subclasses. Math. Nachr., 285: 1770–1790. doi: 10.1002/mana.201100247

Author Information

  1. Mathematisches Institut, Universität Leipzig, Augustusplatz 10/11, 04109 Leipzig, Germany

*Phone: +49-(0)341-97 32106, Fax: +49-(0)341-97 32199

  1. †

    Dedicated to Eduard Ruvimovich Tsekanovskiĭ on the event of his 75th birthday

Publication History

  1. Issue published online: 2 OCT 2012
  2. Article first published online: 11 APR 2012
  3. Manuscript Accepted: 15 NOV 2011
  4. Manuscript Revised: 3 NOV 2011
  5. Manuscript Received: 16 SEP 2011

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Keywords:

  • Matrix-valued Herglotz-Nevanlinna functions;
  • Integral representations;
  • Moore-Penrose pseudoinverse MSC (2010) 30E05;
  • 44A60;
  • 47A57

Abstract

The paper deals with particular subclasses of the class of matrix-valued Herglotz-Nevanlinna functions. Characterizations of these subclasses via integral representations will be presented. Particular emphasis is placed on the discussion of the Moore-Penrose pseudoinverse of these matrix-valued functions.

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