J-Contractive Matrix Valued Functions And Related Topics

by Damir Z. Arov, Harry Dym

• ISBN13: 9780521883009
• ISBN10: 0521883008
• Format: Hardcover
• Copyright: 2008-12-15
• Publisher: Cambridge University Press

Summary

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.

Table of Contents

Introduction	p. 1
Algebraic preliminaries	p. 13
The Nevanlinna class of meromorphic mvf's	p. 83
J-contractive and J-inner matrix valued functions	p. 169
Reproducing kernel Kilbert spaces	p. 240
Operator nodes and passive systems	p. 334
Generalized interpolation problems	p. 358
Generalized Krein extension problems	p. 420
Darlington representations and related inverse problems	p. 470
More criteria for strong regularity	p. 515
Formulas for entropy functionals	p. 536
Bibliography	p. 551
Notation index	p. 567
Subject index	p. 571
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