Katsenelenbaum B.Z. Electromagnetic Fields - Restrictions and Approximation

Weinheim: Wiley-VCH Verlag. – 2003. – 229 p. The subject of this book falls within the scope of three disciplines – the antennas theory, highfrequency electrodynamics and mathematical physics. There are problems in which these disciplines are fundamentally connected. They are the inverse problems of the high-frequency field theory, more precisely – the connection between the shape of the domain in which the monochromatic currents are located, and the possibility of approximating any given field by the fields of these currents. This connection gives rise to a number of profound questions. Many of them are formulated, and some are even solved in this book. The following problems are considered: Antenna synthesis. Optimal current synthesis. Solvability of the first-kind integral equations. Noncompleteness of the set of functions generated by the operator acting over the complete set of functions. Construction of a real solution to the Helmholtz equation (or the Maxwell equations) by its zero line (zero surface). Investigation of pseudo-solutions to the first-kind equations originating from the inverse problems for the fields obtained by the two-dimensional Fourier transformation in arbitrary domains.Nonapproximability of Patterns
Nonapproximability of Near Fields
The Norm of the Current
Electromagnetic Field. The Maxwell Equations
Long Narrow Beam of Electromagnetic WavesAppendix: Antenna Synthesis by Amplitude Radiation Pattern and Modified Phase Problem
Synthesis of Antennas by Amplitude Radiation Pattern
Bibliography for Appendix