Operator Theory for Electromagnetics - Hanson, George W.;Yakovlev, Alexander B.
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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…mehr

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Produktbeschreibung
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.
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 topics in a logical manner. Examples principally geared toward electromagnetics are provided. With the exception of Chapter 1, which serves as a review of basic electromagnetic theory, Part I presents definitions and theorems along with associated discussion and examples. This style was chosen because it allows one to readily identify the main concepts in a particular section. A proof is provided for all theorems whose proof is simple and straightforward. A proof is also provided for theorems that require a slightly more elaborate proof, yet one that is especially enlightening, being either constructive or illustrative. Generally. theorems are stated but not proved in cases where either the proof is too involved or the details of the proof would take one too far afield of the topic at hand, such as requiring additional lemmas that are not clearly useful in applications.
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