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This book covers the latest problems of modern mathematical methods for three-dimensional problems of diffraction by arbitrary conducting screens. This comprehensive study provides an introduction to methods of constructing generalized solutions, elements of potential theory, and other underlying mathematical tools. The problem settings, which turn out to be extremely effective, differ significantly from the known approaches and are based on the original concept of vector spaces 'produced' by Maxwell equations. The formalism of pseudodifferential operators enables to prove uniqueness theorems and the Fredholm property for all problems studied. Readers will gain essential insight into the state-of-the-art technique of investigating three-dimensional problems for closed and unclosed screens based on systems of pseudodifferential equations. A detailed treatment of the properties of their kernels, in particular degenerated, is included. Special attention is given to the study of smoothness of generalized solutions and properties of traces.
Introduction
Diffraction by Cylindrical Screens
Statement of the Problems of Diffraction by Cylindrical Screens
Closed Cylindrical Screens
Unclosed Cylindrical Screens
Diffraction by a Bounded Planar Screen
Statement of the Diffraction Problem and The Uniqueness Theorem
Vector Spaces W and W'
Vector Potentials and Representation of Solutions
Reduction of the Problem to the System of Pseudodifferential Equations
Fredholm Property and Solvability of the System of Pseudodifferential Equations
Smoothness of Generalized Solutions. The Orders of Singularity in the Vicinities of Edges
Diffraction by a System of Arbitrary Bounded Screens
The Spaces W and W' of the Cross Sections of Vector Bundles Over Ω
Representation of Solutions and The System of Integrodifferential Equations on Screens
Reduction of the Problem to the Vector Pseudodifferential Equation on Ω
Fredholm Property and Solvability of the Vector Pseudodifferential Equation
Principle of Limiting Absorption
The Problems of Diffraction in Domains Connected Through a Hole in a Screen
Green’s Functions for Canonical Domains
Vector Integrodifferential Equation on Ω
Diffraction by a Hole in a Planar Screen
Diffraction by a Partially Shielded Layer
Diffraction by an Aperture in a Semi-Infinite Waveguide
References