The Herglotz-Nevanlinna Functions and Rigged Canonical Systems
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.
KeywordsHilbert Space Regular Point Symmetric Operator Canonical System Impedance Function
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