Wednesday, 06 April 2022 17:27

Conservative Realizations of Herglotz-Nevanlinna Functions

  • Author(s): Yuri Arlinskii (East Ukrainian National University, Lugansk, Ukraine), Sergey Belyi (Troy University, USA) Eduard Tsekanovskii (Niagara University, USA)
  • Publisher: Birkhäuser
  • Year: 2011

[Y. Arlinskii, S. Belyi, E. Tsekanovskii, Conservative realizations of Herglotz-Nevanlinna functions, Birkhäuser, Basel, 2011]

This book is devoted to conservative realizations of various classes of Stieltjes, inverse Stieltjes, and general Herglotz-Nevanlinna functions as impedance functions of linear systems. The main feature of the monograph is a new approach to the realization theory profoundly involving developed extension theory in triplets of rigged Hilbert spaces and unbounded operators as state-space operators of linear systems. The connections of the realization theory to systems with accretive, sectorial, and contractive state-space operators as well as to the Phillips-Kato sectorial extension problem, the Krein-von Neumann and Friedrichs extremal extensions are provided. Among other results the book contains applications to the inverse problems for linear systems with non-self-adjoint Schrödinger operators, Jacobi matrices, and to the Nevanlinna-Pick system interpolation.