Reducing the description of arbitrary wave field converters to tensor form

It is shown that solving problems of radio holography, including diagnostics of subsurface objects, actualizes the development of new approaches to solving classical problems of mathematical physics, in particular, the boundary value problem, on the solution of which the description of wave propagation is based. It is shown that the boundary value problem of mathematical physics, corresponding to the theoretical description of the propagation of wave disturbances, can be solved without using the apparatus of Green's functions (fundamental solutions of the wave equation). The basis for this is the description of wave propagation in terms of spatial frequency spectra, based directly on the analysis of the wave equation. This approach makes it possible to justify the use of the concept of a finite Green's function, which remains bounded everywhere. The expediency of using the concept of “wave field converter” is substantiated. It is proven that by excluding inhomogeneous (damped) waves from consideration, the description of an arbitrary radiation converter can be reduced to a discrete (tensor) form. The possibilities of practical use of the proposed approach are discussed, including for the diagnosis of subsurface objects using radio holography methods.