The Herglotz-Nevanlinna Functions and Rigged Canonical Systems

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


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.


Hilbert Space Regular Point Symmetric Operator Canonical System Impedance Function 
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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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