Nonlocal continuum field theories are concerned with material bodies whose behavior at any interior point depends on the state of all other points in the body -- rather than only on an effective field resulting from these points -- in addition to its own state and the state of some calculable external field. Nonlocal field theory extends classical field theory by describing the responses of points within the medium by functionals rather than functions (the "constitutive relations" of classical field theory). Such considerations are already well known in solid-state physics, where the nonlocal...

The purpose of this book is to describe methods for solving problems in applied electromagnetic theory using basic concepts from functional anal ysis and the theory of operators. Although the book focuses on certain mathematical fundamentals, it is written from an applications perspective for engineers and applied scientists working in this area. Part I is intended to be a somewhat self-contained introduction to op erator theory and functional analysis, especially those elements necessary for application to problems in electromagnetics. The goal of Part I is to ex plain and synthesize these...