(Ebook) Conservative realizations of Herglotz-Nevanlinna functions by Yuri Arlinskii, Sergey Belyi, Eduard Tsekanovskii (auth.) ISBN 9783764399955, 3764399953

(Ebook) Conservative realizations of Herglotz-Nevanlinna functions by Yuri Arlinskii, Sergey Belyi, Eduard Tsekanovskii (auth.) ISBN 9783764399955, 3764399953

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.