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  1. Home
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  3. Bitangential Direct and Inverse Problems for Systems of Integral and Differential Equations
  • Cited by 26
  • Damir Z. Arov, South-Ukrainian National Pedagogical University, Odessa, Harry Dym, Weizmann Institute of Science
Publisher:
Cambridge University Press
Online publication date:
October 2012
Print publication year:
2012
Online ISBN:
9781139093514
DOI:
https://doi.org/10.1017/CBO9781139093514
Subjects:
Mathematics (general), Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory, Mathematical Physics
Series:
Encyclopedia of Mathematics and its Applications (145)
Information

Book description

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.

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 Source: Mathematical Reviews

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