Regularization of the problem of diffraction of an arbitrary electromagnetic wave by a perfectly conducting spherical cap (Q1569344)

The authors have proposed a method for the problem of diffraction of an arbitrary electromagnetic wave by an infinitely thin perfectly conducting spherical shell with a circular aperture. A regularization technique is constructed that equivalently reduces the original boundary value problem to a set of algebraic equations of the second kind of the form \((I+H)x=b\) in \(l_2\), where \(x,b\in{l_2}\) and the operator \(H\) is compact in \(l_2\). The technique is based on the method of solving a new class of dual series equations.