Conservative Realizations of Herglotz-Nevanlinna Functions (Operator Theory: Advances and Applications Book 217) 2011th Edition by Yuri Arlinskii (PDF)

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    Ebook Info

    • Published: 2011
    • Number of pages: 548 pages
    • Format: PDF
    • File Size: 4.58 MB
    • Authors: Yuri Arlinskii

    Description

    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.

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