  Most of the known Fourier transforms associated with the equations of
mathematical physics have a trivial kernel, and an inversion formula as well as
the Parseval equality are fulfilled. In other words, the system of the
eigenfunctions involved in the definition of the integral transform is
complete. Here we will study Fourier transform associated with the differential
operator, which in addition to the continuous part of the spectrum that defines
this transform, may contain a set of eigenfunctions. These functions become the
elements of the kernel of Fourier transform.
