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...

This volume deals with the Cauchy or initial value problem for linear differential equations. It treats in detail some of the applications of linear space methods to partial differential equations, especially the equations of mathematical physics such as the Maxwell, Schrodinger and Dirac equations. Background material presented in the first chapter makes the book accessible to mathematicians and physicists who are not specialists in this area as well as to graduate students."