Research Catalog

Title

J-contractive matrix valued functions and related topics / Damir Z. Arov and Harry Dym.

Author

Arov, Damir Z.

Publication

Cambridge : Cambridge University Press, 2008.

Items in the Library & Off-site

Details

Additional Authors

Dym, H. (Harry), 1938-

Description

xi, 575 p.; 25 cm.

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.

Series Statement

Encyclopedia of mathematics and its applications ; 116

Uniform Title

Encyclopedia of mathematics and its applications ; v. 116

Subject

• Functions of complex variables
• Matrices

Bibliography (note)

• Includes bibliographical references and index.

Processing Action (note)

• committed to retain

Contents

1. Introduction -- 2. Algebraic preliminaries -- 3. Nevanlinna class of meromorphic mvf's -- 4. J-contractive and J-inner matrix valued functions -- 5. Reproducing kernel Kilbert spaces -- 6. Operator nodes and passive systems -- 7. Generalized interpolation problems -- 8. Generalized Krein extension problems -- 9. Darlington representations and related inverse problems -- 10. More criteria for strong regularity -- 11. Formulas for entropy functionals.

ISBN

• 9780521883009 (hbk.)
• 0521883008 (hbk.)

OCLC

• 173238949
• SCSB-10353049

Owning Institutions

Harvard Library