Weak radiation condition in the problem of a plane wave diffraction by a wedge

The Kontorovich-Lebedev transform is used for the solution of various problems of diffraction by a wedge. A failure of this transform is that it is applicable to a narrow class of functions not containing, in particular, a complete solution to the problem of diffraction. To overcome this problem a modified Kontorovich-Lebedev transform has previously been obtained in which the two-dimensional equation is reduced to an ordinary differential equation. The authors obtain a generalized radiation condition to give sense to this equation for the problem of plane wave diffraction by a wedge