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On Reciprocal Sequences of Matricial Carathéodory Sequences and Associated Matrix Functions

  • Bernd FritzscheEmail author
  • Bernd Kirstein
  • Andreas Lasarow
  • Armin Rahn
Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 226)

Abstract

This paper provides a detailed discussion of reciprocal sequences of finite and infinite matricial Carathodory sequences, including an examination of the relationship a reciprocal sequence has to its original sequence. The properties of such reciprocal sequences are described. Of particular interest is the fact that the reciprocal sequence of a Carathodory sequence is again a Carathodory sequence. Later, these results are applied to matrix-valued functions. The natural focus is, in particular, on the matricial Carathodory functions associated with a matricial Carathodory sequence and its reciprocal sequence. These matrix functions are then shown to be Moore-Penrose inverses of each other. The implications of these results for non-negative Hermitian matrix measures on the unit circle are also discussed.

Keywords

Reciprocal sequences Moore-Penrose inverse matrix-valued Carathodory functions 

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Copyright information

© Springer Basel 2012

Authors and Affiliations

  • Bernd Fritzsche
    • 1
    Email author
  • Bernd Kirstein
    • 1
  • Andreas Lasarow
    • 1
  • Armin Rahn
    • 1
  1. 1.Mathematisches InstitutUniversität LeipzigLeipzigGermany

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