Custom cover image
Conservative Realizations of Herglotz-Nevanlinna Functions / by Yuri Arlinskii, Sergey Belyi, Eduard Tsekanovskii
Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Operator Theory: Advances and Applications ; 217 | SpringerLink BücherPublisher: Basel : Springer Basel AG, 2011Description: Online-Ressource (XVIII, 528p. 21 illus., 1 illus. in color, digital)ISBN:- 9783764399962
- 003 515.724
- 515.724
- QA329-329.9
- QA39.3
Contents:
Summary: 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.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 Schrödinger operators, Jacobi matrices, and to the Nevanlinna-Pick system interpolation.PPN: PPN: 1650972636Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-SMA
Conservative Realizations of Herglotz-Nevanlinna Functions; Preface; Contents; Chapter 1 Extensions of Symmetric Operators; Chapter 2 Geometry of Rigged Hilbert Spaces; Chapter 3 Bi-extensions of Closed Symmetric Operators; Chapter 4 Quasi-self-adjoint Extensions; Chapter 5 The Livšic Canonical Systems with Bounded Operators; Chapter 6 The Herglotz-Nevanlinna Functions and Rigged Canonical Systems; Chapter 7 Classes of realizable Herglotz-Nevanlinna functions; Chapter 8 Normalized L-Systems; Chapter 9 Canonical L-systems with Contractive and Accretive Operators
Chapter 10 L-systems with Schrödinger operatorChapter 11 Non-self-adjoint Jacobi Matrices and System Interpolation; Chapter 12 Non-canonical Systems; Notes and Comments; Bibliography; Index;
No physical items for this record