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 Schr?dinger operators,? Jacobi matrices, and to the Nevanlinna-Pick system interpolation.
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.
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 Schr?dinger operator.- 11 Non-self-adjoint Jacobi Matrices and System Interpolation.- 12 Non-canonical Systems.- Notes and Comments.- References.- Index.
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 l4
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