Synopses & Reviews
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
Review
From the reviews: "The book demonstrates the deep and powerful interconnection between operator theory, systems theory, and the theory of analytic functions of one variable (which was observed and explored in the pioneering works of M. Livšic). It will be of interest for researchers in each of these fields." (Dmitry Kaliuzhnyi-Verbovetskyi, Zentralblatt MATH, Vol. 1240, 2012)
Review
From the reviews:"The book demonstrates the deep and powerful interconnection between operator theory, systems theory, and the theory of analytic functions of one variable (which was observed and explored in the pioneering works of M. Livšic). It will be of interest for researchers in each of these fields." (Dmitry Kaliuzhnyi-Verbovetskyi, Zentralblatt MATH, Vol. 1240, 2012)
Synopsis
This book covers the realization theory of various classes of Stieltjes, inverse Stieltjes and general Herglotz-Nevanlinna functions as linear fractional transformations of transfer functions of linear conservative systems.
Table of Contents
Preface.- 1 Extensions of Symmetric Operators.- 2 Rigged Hilbert Spaces.- 3 Bi-extensions of Closed Symmetric Operators.-.4 Quasi-self-adjoint Extensions.- 5 The Livsic Canonical Systems with Bounded Operators.- 6 Herglotz-Nevanlinna functions and Rigged Canonical Systems.- 7 Classes of realizable Herglotz-Nevanlinna functions.- 8 Normalized Canonical Systems.- 9 Canonical L-systems with Contractive and Accretive Operators.- 10 Systems with Schrödinger operator.- 11 Non-self-adjoint Jacobi Matrices and System Interpolation.- 12 Non-canonical Systems.- Notes and Comments.- References.- Index.