J-Contractive Matrix Valued Functions and Related Topics

A comprehensive introduction to the theory of J-contractive and J-inner matrix valued functions.

Damir Z. Arov (Author), Harry Dym (Author)

9780521883009, Cambridge University Press

Hardback, published 6 November 2008

588 pages, 4 tables
24 x 16.5 x 3.5 cm, 0.98 kg

'… well written with theoretical results of a high standard … can be recommended to scientists, engineers and students preparing their doctoral theses.' EMS Newsletter

J-contractive and J-inner matrix valued functions have a wide range of applications in mathematical analysis, mathematical physics, control engineering and theory of systems and networks. This book provides a comprehensive introduction to the theory of these functions with respect to the open upper half-plane, and a number of applications are also discussed. The first chapters develop the requisite background material from the geometry of finite dimensional spaces with an indefinite inner product, and the theory of the Nevanlinna class of matrix valued functions with bounded characteristic in the open upper half-plane (with attention to special subclasses). Subsequent chapters develop this theory to include associated pairs of inner matrix valued functions and reproducing kernel Hilbert spaces. Special attention is paid to the subclasses of regular and strongly regular J-inner matrix valued functions, which play an essential role in the study of the extension and interpolation problems.

Preface
1. Introduction
2. Algebraic preliminaries
3. The Nevanlinna class of meromorphic mvf's
4. J-contractive and J-inner matrix valued functions
5. Reproducing kernel Hilbert spaces
6. Generalized interpolation problems
7. Generalized Krein extension problems
8. Darlington representations and related inverse problems
9. More criteria for strong regularity
10. Formulas for entropy functionals
Bibliography.

Subject Areas: Calculus & mathematical analysis [PBK]