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The Herglotz-Nevanlinna Functions and Rigged Canonical Systems

  • Yuri Arlinskii
  • Sergey Belyi
  • Eduard Tsekanovskii
Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 217)

Abstract

In this chapter we focus on Herglotz-Nevanlinna functions. After providing all the preliminary results, we introduce the Livšic rigged canonical system (L-system) and its impedance function. We find the necessary and sufficient conditions for a given Herglotz-Nevanlinna function to be realized as the impedance function of an L-system. The properties of the state-space operator of an L-system based on a given impedance function are determined.

Keywords

Hilbert Space Regular Point Symmetric Operator Canonical System Impedance Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  • Yuri Arlinskii
    • 1
  • Sergey Belyi
    • 2
  • Eduard Tsekanovskii
    • 3
  1. 1.Department of MathematicsEast Ukrainian National UniversityLuganskUkraine
  2. 2.Department of MathematicsTroy UniversityTroyUSA
  3. 3.Department of MathematicsNiagara UniversityLewistonUSA

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