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|a 9783764399962
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|a Arlinskii, Yuri
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| 245 |
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|a Conservative Realizations of Herglotz-Nevanlinna Functions
|h Elektronische Ressource
|c by Yuri Arlinskii, Sergey Belyi, Eduard Tsekanovskii
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| 250 |
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|a 1st ed. 2011
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| 260 |
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|a Basel
|b Birkhäuser
|c 2011, 2011
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| 300 |
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|a XVIII, 530 p
|b online resource
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| 505 |
0 |
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|a 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
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| 653 |
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|a Operator theory
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| 653 |
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|a Mathematical physics
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| 653 |
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|a Operator Theory
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| 653 |
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|a Mathematical Methods in Physics
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| 700 |
1 |
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|a Belyi, Sergey
|e [author]
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| 700 |
1 |
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|a Tsekanovskii, Eduard
|e [author]
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| 041 |
0 |
7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b Springer
|a Springer eBooks 2005-
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| 490 |
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|a Operator Theory: Advances and Applications
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| 028 |
5 |
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|a 10.1007/978-3-7643-9996-2
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| 856 |
4 |
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|u https://doi.org/10.1007/978-3-7643-9996-2?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
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|a 515.724
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| 520 |
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|a 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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