Conservative realizations of Herglotz-Nevanlinna functions
- Yuri Arlinskii, Sergey Belyi, Eduard Tsekanovskii.
- New York : Springer, c2011.
- Physical description
- xviii, 528 p. : ill. ; 24 cm.
- Operator theory, advances and applications ; v. 217.
Math & Statistics Library
QA39.3 .A75 2011
- Unknown QA39.3 .A75 2011
- Includes bibliographical references and index.
- 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 Schrodinger operator.- 11 Non-self-adjoint Jacobi Matrices and System Interpolation.- 12 Non-canonical Systems.- Notes and Comments.- References.- Index.
- (source: Nielsen Book Data)
- Publisher's Summary
- 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 Schrodinger operators, Jacobi matrices, and to the Nevanlinna-Pick system interpolation.
(source: Nielsen Book Data)
- Publication date
- Operator theory, advances and applications ; v. 217