Overview
- Only book covering this spectrum of problems and methods of the Herglotz-Nevanlinna functions realization
- First comprehensive coverage of the realization theory for Herglotz-Nevanlinna matrix functions
- Contains useful and important applications
- Includes supplementary material: sn.pub/extras
Part of the book series: Operator Theory: Advances and Applications (OT, volume 217)
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Table of contents (12 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Reviews
From the reviews:
“The book demonstrates the deep and powerful interconnection between operator theory, systems theory, and the theory of analytic functions of one variable (which was observed and explored in the pioneering works of M. Livšic). It will be of interest for researchers in each of these fields.” (Dmitry Kaliuzhnyi-Verbovetskyi, Zentralblatt MATH, Vol. 1240, 2012)Authors and Affiliations
Bibliographic Information
Book Title: Conservative Realizations of Herglotz-Nevanlinna Functions
Authors: Yuri Arlinskii, Sergey Belyi, Eduard Tsekanovskii
Series Title: Operator Theory: Advances and Applications
DOI: https://doi.org/10.1007/978-3-7643-9996-2
Publisher: Birkhäuser Basel
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Basel AG 2011
Hardcover ISBN: 978-3-7643-9995-5Published: 23 June 2011
Softcover ISBN: 978-3-0348-0333-5Published: 03 August 2013
eBook ISBN: 978-3-7643-9996-2Published: 21 June 2011
Series ISSN: 0255-0156
Series E-ISSN: 2296-4878
Edition Number: 1
Number of Pages: XVIII, 530