Bitangential Direct and Inverse Problems for Systems of Integral and Differential Equations (Encyclopedia of Mathematics and its Applications)
Cambridge University Press, 9/13/2012
EAN 9781107018877, ISBN10: 1107018870
Hardcover, 488 pages, 23.4 x 15.6 x 3.2 cm
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.
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. Dirac–Krein systems
Bibliography
Index.