Bitangential Direct and Inverse Problems for Systems of Integral and Differential Equations

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Damir Z. Arov Harry Dym

Bitangential Direct and Inverse Problems for Systems of Integral and Differential Equations

Damir Z. Arov, Harry Dym

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English

Cambridge University Press
13 September 2012

Mathematics & Sciences; Differential calculus & equations

Series: Encyclopedia of Mathematics and its Applications

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.

By: Damir Z. Arov, Harry Dym
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 145
Dimensions: Height: 234mm, Width: 156mm, Spine: 32mm
Weight: 880g
ISBN: 9781107018877
ISBN 10: 1107018870
Series: Encyclopedia of Mathematics and its Applications
Pages: 488
Publication Date: 13 September 2012
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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.

Reviews for Bitangential Direct and Inverse Problems for Systems of Integral and Differential Equations

'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