The rigorous solution of the two-dimensional problem of diffraction by a finite number of curvilinear screens

A rigorous solution of the problem of the diffraction of a plane electromagnetic wave by a finite number of circular cylinders with longitudinal slits is discussed. The initial problem in terms of differential equations is reduced to an analysis of the operator equation of the second kind with a totally continuous operator. The unique solvability of the equation obtained, and the equivalence theorem are proved.