Bitangential direct and inverse problems for systems of integral and differential equations [EBook] / Damir Z. Arov, Harry Dym.
Bitangential direct and inverse problems for systems of integral and differential equations [EBook] / Damir Z. Arov, Harry Dym.
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 mo...
Personal Name(s):  Arov, Damir Z., (author) 

Dym, Harry, (author)  
Imprint: 
Cambridge :
Cambridge University Press,
2012

Physical Description: 
1 online resource (xiv, 472 pages) 
Note: 
englisch 
ISBN: 
9781139093514 9781107018877 
Series Title: 
Encyclopedia of mathematics and its applications ;
volume 145 
Subject (LOC):  
Full Text 
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. 