|
REALIZABILITY THEORY FOR CONTINUOUS LINEAR SYSTEMS |
| SHORT DESCRIPTION OF THE BOOK This book offers a thorough and 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. Chapters 1 and 2 cover vector-valued functions, and integration with vector-valued functions and operator-valued measures. Chapter 3 addresses Banach-space-valued testing functions and distributions. Chapter 4 through 8 explore systems theory in kernel operators, convolution operators, the Laplace transformation, and the scattering and admittance formulisms. The book will be of 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 appendices. |
