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 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 of the cross sections of vector bundles over Representation of solutions and the system of integrodifferential equations on screens Reduction of the problem to the vector pseudodifferential equation on 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 Diffraction by a hole in a planar screen Diffraction by a partially shielded layer Diffraction by an aperture in a semi-infinite waveguide REFERENCES