Differential operator related to the generalized superradiance integral equation

In this paper we consider a class of problems which are generalized versions of the three-dimensional superradiance integral equation. A commuting differential operator will be found for this generalized problem. For the three-dimensional superradiance problem an alternative set of complete eigenfunctions will also be provided. The kernel for the superradiance problem when restricted to one-dimension is the same as appeared in the works of Slepian, Landau and Pollak (cf. Slepian and Pollak (1961) [1], Landau and Pollak (1961, 1962) [2,3], Slepian (1964, 1978) [4,5]). The uniqueness of the differential operator commuting with that kernel is indicated.