The authors study the singular system belonging to a truncated Laplace transform L whose inverse has compact, strictly positive support, and its adjoint. The eigenfunctions of \(L^*L\) are found to be those of a certain differential operator; the authors study these with the objective of applying them to the inversion of the transform, as studied, for example, by the first author, P. Brianzi and E. Pike [ibid. 1, 1-15 (1985; reviewed above)].