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Operator Theory: Advances and Applications

Conservative Realizations of Herglotz-Nevanlinna Functions

Authors: Arlinskii, Yuri, Belyi, Sergey, Tsekanovskii, Eduard

  • 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
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eBook $109.00
price for USA in USD (gross)
  • ISBN 978-3-7643-9996-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.99
price for USA in USD
  • ISBN 978-3-7643-9995-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.99
price for USA in USD
  • ISBN 978-3-0348-0333-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
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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)

Table of contents (12 chapters)

  • Extensions of Symmetric Operators

    Arlinskii, Yuri (et al.)

    Pages 1-21

  • Geometry of Rigged Hilbert Spaces

    Arlinskii, Yuri (et al.)

    Pages 23-43

  • Bi-extensions of Closed Symmetric Operators

    Arlinskii, Yuri (et al.)

    Pages 45-68

  • Quasi-self-adjoint Extensions

    Arlinskii, Yuri (et al.)

    Pages 69-118

  • The Livšsic Canonical Systems with Bounded Operators

    Arlinskii, Yuri (et al.)

    Pages 119-145

Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-3-7643-9996-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.99
price for USA in USD
  • ISBN 978-3-7643-9995-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.99
price for USA in USD
  • ISBN 978-3-0348-0333-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Conservative Realizations of Herglotz-Nevanlinna Functions
Authors
Series Title
Operator Theory: Advances and Applications
Series Volume
217
Copyright
2011
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel AG
eBook ISBN
978-3-7643-9996-2
DOI
10.1007/978-3-7643-9996-2
Hardcover ISBN
978-3-7643-9995-5
Softcover ISBN
978-3-0348-0333-5
Series ISSN
0255-0156
Edition Number
1
Number of Pages
XVIII, 530
Topics