Conservative Realizations of Herglotz-Nevanlinna Functions [recurso electrónico] / by Yuri Arlinskii, Sergey Belyi, Eduard Tsekanovskii.

Por: Arlinskii, Yuri [author.]Colaborador(es): Belyi, Sergey [author.] | Tsekanovskii, Eduard [author.] | SpringerLink (Online service)Tipo de material: TextoTextoSeries Operator Theory: Advances and Applications ; 217Editor: Basel : Springer Basel, 2011Descripción: XVIII, 530 p. online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9783764399962Tema(s): Mathematics | Operator theory | Mathematical physics | Mathematics | Operator Theory | Mathematical Methods in PhysicsFormatos físicos adicionales: Printed edition:: Sin títuloClasificación CDD: 515.724 Clasificación LoC:QA329-329.9Recursos en línea: Libro electrónicoTexto
Contenidos:
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.
En: Springer eBooksResumen: 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.
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Colección de Libros Electrónicos QA329 -329.9 (Browse shelf(Abre debajo)) 1 No para préstamo 377029-2001

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.

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.

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