Bitangential direct and inverse problems for systems of integral and differential equations
 Author/Creator
 Arov, Damir Z.
 Language
 English.
 Imprint
 Cambridge, UK ; New York : Cambridge University Press, 2012.
 Physical description
 xiv, 472 p. : ill. ; 24 cm.
 Series
 Encyclopedia of mathematics and its applications ; 145.
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Contributors
 Contributor
 Dym, Harry, 1934
Contents/Summary
 Bibliography
 Includes bibliographical references (p. [450]464) and indexes.
 Contents

 Machine generated contents note: 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. DiracKrein systems; Bibliography; Index.
 Summary
 "This largely selfcontained 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 Jinner 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 selfstudy. A number of examples are presented to illustrate the theory" Provided by publisher.
 "This largely selfcontained 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 matrixvalued spectral function, or an asymptotic scattering matrix. The corresponding direct problems are also treated. The book incorporates introductions to the theory of matrixvalued entire functions, reproducing kernel Hilbert spaces of vectorvalued entire functions (with special attention to two important spaces introduced by L. de Branges), the theory of Jinner matrixvalued functions and their application to bitangential interpolation and extension problems, which can be used independently for courses and seminars in analysis or for selfstudy. A number of examples are presented to illustrate the theory" Provided by publisher.
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Bibliographic information
 Publication date
 2012
 Responsibility
 Damir Z. Arov, Harry Dym.
 Series
 Encyclopedia of mathematics and its applications ; 145
 ISBN
 9781107018877
 1107018870