Description
Conservative Realizations of Herglotz-Nevanlinna Functions, 2011
Operator Theory: Advances and Applications Series, Vol. 217
Authors: Arlinskii Yuri, Belyi Sergey, Tsekanovskii Eduard
Language: English105.49 €
In Print (Delivery period: 15 days).
Add to cart the book of Arlinskii Yuri, Belyi Sergey, Tsekanovskii EduardPublication date: 08-2013
530 p. · 15.5x23.5 cm · Paperback
105.49 €
In Print (Delivery period: 15 days).
Add to cart the book of Arlinskii Yuri, Belyi Sergey, Tsekanovskii EduardPublication date: 06-2011
530 p. · 15.5x23.5 cm · Hardback
Description
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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.
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.