Operator Theory: Advances and Applications

Arlinskii, Yuri; Belyi, Sergey; Tsekanovskii, Eduard

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.

Details

Published by: Birkhäuser

Publication Date: 2011-06-23

Format: Hardcover

ISBN-13: 9783764399955

DOI: 10.1007/978-3-7643-9996-2

Dimensions: 235cm x155cm

Pages: 530