Conservative Realizations of Herglotz-Nevanlinna FunctionsSpringer Science & Business Media, 21 de juny 2011 - 530 pàgines 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. |
Continguts
1 | |
Chapter 2 Geometry of Rigged Hilbert Spaces | 23 |
Chapter 3 Biextensions of Closed Symmetric Operators | 44 |
Chapter 4 Quasiselfadjoint Extensions | 69 |
Chapter 5 The Livšic Canonical Systems with Bounded Operators | 119 |
Chapter 6 The HerglotzNevanlinna Functions and Rigged Canonical Systems | 147 |
Chapter 7 Classes of realizable HerglotzNevanlinna functions | 204 |
Chapter 8 Normalized LSystems | 239 |
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Conservative Realizations of Herglotz-Nevanlinna Functions Yuri Arlinskii,Sergey Belyi,Eduard Tsekanovskii Previsualització no disponible - 2011 |
Conservative Realizations of Herglotz-Nevanlinna Functions Yuri Arlinskii,Sergey Belyi,Eduard Tsekanovskii Previsualització no disponible - 2013 |