## Operator Theory for Electromagnetics: An IntroductionThe 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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### Contents

Electromagnetic Fundamentals | 3 |

Introductory Functional Analysis | 63 |

Bibliography | 125 |

Bibliography | 213 |

Spectral Theory of Linear Operators | 219 |

Bibliography | 287 |

Bibliography | 363 |

TransmissionLine Analysis | 403 |

Cylindrical Waveguide Problems | 503 |

Planarly Layered Medium | 553 |

Electromagnetic Cavities | 575 |

597 | |

A Vector Dyadic and Integral Relations | 605 |

B Derivation of SecondDerivative Formula 1 59 | 615 |

Coefficients of PlanarMedia Greens Dyadics | 621 |

629 | |

### Other editions - View all

Operator Theory for Electromagnetics: An Introduction George W. Hanson,Alexander B. Yakovlev Limited preview - 2013 |

Operator Theory for Electromagnetics: An Introduction George W. Hanson,Alexander B. Yakovlev No preview available - 2011 |

### Common terms and phrases

2ero adjoint analysis apertures applied associated assume basis boundary conditions boundary value problem bounded linear operator bounded operator cavity characteri2ed coefficients compact operator components consider continuous convergence corresponding defined Definition dielectric differential operator Dirichlet discussed domain dyadic Green's function eigenbasis eigenfunction expansion eigenfunctions eigenvalue problem eigenvectors electric field electric Green's dyadics electromagnetics elements example exists finite finite-dimensional spaces generali2ed Green's function Green's theorem Hilbert space homogeneous improper eigenfunctions infinite inner product space integral equations integral operator inverse kernel leads linear operator linear subspace magnetic field matrix operator method metric modes Nenmann norm Note obtained one-dimensional orthogonal orthonormal perfectly conducting potential psendo rectangular waveguide region represents resonance resulting satisfy scalar scattering second kind Section self-adjoint operators sequence shown singular solution spectral spectrum Sturm-Liouville problem surface term theory tions two-dimensional vector wave waveguide

### Popular passages

Page 600 - On the Question of Computation of the Dyadic Green's Function at the Source Region in Waveguides and Cavities,

Page 598 - Frequency Response of Multiconductor Transmission Lines Illuminated by an Electromagnetic Field," IEEE Trans, on Electromagnetic Compatibility.

Page 602 - Zwischenmedium' to the radiation from a flanged waveguide', Proc. IEE, 120.