On the Convergence of the Inverse Diffraction Transform Kernel Using Ces�ro Summability

In tomography, optical information processing and, more generally, Fourier optics, the diffraction transform solves both the direct and the inverse boundary value propagation problem for the Helmholtz equation. Its kernel is itself an integral. It is the representation of the evolution operator associated with translations of a constrained Cartesian coordinate. This fact threatens the inverse scattering problem with a divergenze if the transform kernel is understood as a Cauchy integral. The kernel is, however, everywhere convergent if its integral representation is interpreted as a Cesa'ro summable integral.