Skip to content
Register Sign in Wishlist

J-Contractive Matrix Valued Functions and Related Topics


Part of Encyclopedia of Mathematics and its Applications

  • Authors:
  • Damir Z. Arov, South-Ukrainian Pedagogical University, Odessa, Ukraine
  • Harry Dym, Weizmann Institute of Science, Israel
  • Date Published: November 2008
  • availability: Available
  • format: Hardback
  • isbn: 9780521883009

£ 142.00

Add to cart Add to wishlist

Other available formats:

Looking for an inspection copy?

This title is not currently available on inspection

Product filter button
About the Authors
  • J-contractive and J-inner matrix valued functions have a wide range of applications in mathematical analysis, mathematical physics, control engineering and theory of systems and networks. This book provides a comprehensive introduction to the theory of these functions with respect to the open upper half-plane, and a number of applications are also discussed. The first chapters develop the requisite background material from the geometry of finite dimensional spaces with an indefinite inner product, and the theory of the Nevanlinna class of matrix valued functions with bounded characteristic in the open upper half-plane (with attention to special subclasses). Subsequent chapters develop this theory to include associated pairs of inner matrix valued functions and reproducing kernel Hilbert spaces. Special attention is paid to the subclasses of regular and strongly regular J-inner matrix valued functions, which play an essential role in the study of the extension and interpolation problems.

    • Comprehensive and self contained account of the theory of J-contractive and J-inner matrix valued functions
    • Applications to a variety of problems in mathematical analysis, mathematical physics, control engineering and the mathematical theory of systems and networks
    • Brings together years of research, much by the authors themselves, into book form for the first time
    Read more

    Reviews & endorsements

    '… packed with information, much of which is not readily found elsewhere. The book will surely be useful for many years to come, and the authors are to be congratulated on a valuable contribution to the literature.' Mathematical Reviews

    '… well written with theoretical results of a high standard … can be recommended to scientists, engineers and students preparing their doctoral theses.' EMS Newsletter

    See more reviews

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity


    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?


    Product details

    • Date Published: November 2008
    • format: Hardback
    • isbn: 9780521883009
    • length: 588 pages
    • dimensions: 240 x 165 x 35 mm
    • weight: 0.98kg
    • contains: 4 tables
    • availability: Available
  • Table of Contents

    1. Introduction
    2. Algebraic preliminaries
    3. The Nevanlinna class of meromorphic mvf's
    4. J-contractive and J-inner matrix valued functions
    5. Reproducing kernel Hilbert spaces
    6. Generalized interpolation problems
    7. Generalized Krein extension problems
    8. Darlington representations and related inverse problems
    9. More criteria for strong regularity
    10. Formulas for entropy functionals

  • Authors

    Damir Z. Arov, South-Ukrainian Pedagogical University, Odessa, Ukraine
    Damir Z. Arov is Professor of Mathematical Analysis at South-Ukraine Pedagogical University in Odessa. He is the author of more than 100 research and survey papers and has been an invited speaker at numerous international conferences.

    Harry Dym, Weizmann Institute of Science, Israel
    Harry Dym is Professor Emeritus in the Department of Mathematics at the Weizmann Institute of Science in Israel. He has written more than 100 papers and this is his 5th book. Professor Dym is well know for his work in this area and his research interests are Operator Theory, Interpolation Theory, Inverse Problems and Classical Analysis.

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner Please see the permission section of the catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×
warning icon

Turn stock notifications on?

You must be signed in to your Cambridge account to turn product stock notifications on or off.

Sign in Create a Cambridge account arrow icon

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.


Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

Please fill in the required fields in your feedback submission.