Spectral properties of a differential operator related to the inversion of the finite Laplace transform

Abstract
The authors investigate the spectrum of a differential operator whose eigenfunctions are the singular functions of the finite Laplace transform. They demonstrate a close connection of this operator with the Legendre operator and give results of numerical computations of its eigenvalues and eigenfunctions. The latter are of great relevance in the problem of the finite Laplace transform inversion.