REALIZABILITY THEORY FOR CONTINUOUS LINEAR SYSTEMS

This excellent study offers a thorough, concise exposition of realizability theory as applied to continuous linear systems, specifically to the operators generated by physical systems as mappings of stimuli into responses. Its primary concern is the study of physical properties and their mathematical characterizations but not the design of particular systems.

Chapters 1 kai 2 cover vector-values functions, and integration and vector-valued functions and operator-valued measures. Chapter 3 addresses Banach-space-valued testing functions and distributions. Chapters 4 through 8 explore systems theory in kernel operators, convolution operators, the Laplace transformation and scattering and admittance formulisms.

The book will be of special interest to electrical network theorists, applied mathematicians and physicists, and pure mathematicians interested in the applications of functional analysis. It will be accessible to all readers familiar with introductory courses on real and complex analysis. Other prerequisites, such as topological linear spaces, Bochner integrals and Banach-space-valued distributions, are covered in the text or in the appendixes.

The author has included a number of problems that asks the reader either to supply the proofs of certain assertions that were made – but not proved – in the text, or to extend the theory in various ways.

Republication of the book originally published by Academic Press, 1972.