Edge Green’s functions on a branched surface. Asymptotics of solutions of coordinate and spectral equations

Abstract

The problems of diffraction by a slit or a strip having ideal boundary conditions, and some other problems, can be reduced to the problem of wave propagation on a multisheet surface by applying the method of reflections. Further simplifications of the problem can be achieved by applying an embedding formula. As a result, the solution of the problem with a plane wave incidence becomes expressed in terms of the edge Green’s functions, i.e., in terms of the fields generated by dipole sources localized at branchpoints of the surface.