Operator Theory for Electromagnetics: An Introduction

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While there are many excellent books available on fundamental and applied electromagnetics, few discuss the subject from the view of operator theory, introducing operator theory only when needed. Perhaps this is because the operators associated with dynamic problems are commonly thought to be not well behaved. This is, however, not the case, and many problems in electromagnetic theory can be cast in useful and efficient operator forms.After a brief review of electromagnetic theory, the book begins with a self-contained introduction to operator theory: linear operators, spectral theory, and Sturm-Liouville operators. The discussion is mathematical, presenting definitions and theorems, as well as proofs of the theorems when these are simple or enlightening. The tools developed in the first part are then applied to problems in classical electromagnetic theory: boundary-value problems, transmission lines, layered media, waveguides, and cavities. The emphasis throughout the discussions of both mathematics and applications is on electromagnetics in engineering.