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

Nonfiction, Science & Nature, Science, Physics, Mathematical Physics, Mathematics
Cover of the book Bitangential Direct and Inverse Problems for Systems of Integral and Differential Equations by Damir Z. Arov, Harry Dym, Cambridge University Press
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Author: Damir Z. Arov, Harry Dym ISBN: 9781107264182
Publisher: Cambridge University Press Publication: September 13, 2012
Imprint: Cambridge University Press Language: English
Author: Damir Z. Arov, Harry Dym
ISBN: 9781107264182
Publisher: Cambridge University Press
Publication: September 13, 2012
Imprint: Cambridge University Press
Language: English

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.

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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.

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