J-Contractive Matrix Valued Functions and Related Topics (Encyclopedia of Mathematics and its Applications Book 116) by Damir Z. Arov (PDF)

Description

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.

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⭐Instead of delving immediately into the mathematics of J-contractive matrices, the author should spend more time in the beginning and in the middle pointing out the general position of this topic within the world of symplectic transformations in classical physics and dissipation in electrical engineering. Many seemingly totally unmotivated topics would become clear.

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