Development of the methods of analytic regularization in the theory of diffraction

We present a survey of works devoted to the development of the methods of analytic regularization for the solutions of mixed boundary-value problems of the diffraction theory. We consider the problems of diffraction of electromagnetic and acoustic waves on the fragments of conic, wedgelike, and cylindrical perfect surfaces and the problem of diffraction of elastic waves on interface cracks. For the solution of these problems, we develop a method of partial inversion of the operator and apply the Wiener–Hopf technique.