Overview

This largely self-contained treatment surveys, unites and extends some 20 years of research on direct and inverse problems for canonical systems of integral and differential equations and related systems. Five basic inverse problems are studied in which the main part of the given data is either a monodromy matrix; an input scattering matrix; an input impedance matrix; a matrix valued spectral function; or an asymptotic scattering matrix. The corresponding direct problems are also treated. The book incorporates introductions to the theory of matrix valued entire functions, reproducing kernel Hilbert spaces of vector valued entire functions (with special attention to two important spaces introduced by L. de Branges), the theory of J-inner matrix valued functions and their application to bitangential interpolation and extension problems, which can be used independently for courses and seminars in analysis or for self-study. A number of examples are presented to illustrate the theory.

Full Product Details

Author:   Damir Z. Arov ,  Harry Dym
Publisher:   Cambridge University Press
Imprint:   Cambridge University Press (Virtual Publishing)
Volume:   145
ISBN:  

9781139093514

ISBN 10:   1139093517
Publication Date:   05 October 2012
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Undefined
Publisher's Status:   Active
Availability:   In stock  
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Table of Contents

1. Introduction; 2. Canonical systems and related differential equations; 3. Matrix valued functions in the Nevanlinna class; 4. Interpolation problems, resolvent matrices and de Branges spaces; 5. Chains that are matrizants and chains of associated pairs; 6. The bitangential direct input scattering problems; 7. Bitangential direct input impedance and spectral problems; 8. Inverse monodromy problems; 9. Bitangential Krein extension problems; 10. Bitangential inverse input scattering problems; 11. Bitangential inverse input impedance and spectral problems; 12. Dirac–Krein systems; Bibliography; Index.

Reviews

'The book provides a unified setting for understanding and codifying a number of seemingly disparate areas of analysis appearing not only in the authors' earlier work, but also in numerous articles of other authors scattered throughout the literature.' Joseph A. Ball, Mathematical Reviews The book provides a unified setting for understanding and codifying a number of seemingly disparate areas of analysis appearing not only in the authors' earlier work, but also in numerous articles of other authors scattered throughout the literature. Joseph A. Ball, Mathematical Reviews

'The book provides a unified setting for understanding and codifying a number of seemingly disparate areas of analysis appearing not only in the authors' earlier work, but also in numerous articles of other authors scattered throughout the literature.' Joseph A. Ball, Mathematical Reviews

Author Information

Damir Z. Arov is Professor in the Division of Applied Mathematics and Informatics at the South-Ukrainian Pedagogical University, Odessa. Harry Dym is Professor Emeritus in the Department of Mathematics at the Weizmann Institute of Science, Rehovot, Israel.

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