On the necessary condition when the homogeneous Helmholtz equation satisfies the Sommerfeld radiation condition

The paper presents the necessary condition providing that the homogeneous Helmholtz equation solution determined by a preset plane boundary condition satisfies the Sommerfeld radiation condition. We have shown that this is a condition of double-continuous differentiability of the product of cosine of angle of incidence by the two-dimensional Fourier-image of field on the specified plane in spherical coordinates. This makes it possible to correctly solve such problems as, for instance, determination of radiation pressure upon particles in an arbitrary incident field.