  An exact inversion formula for the Lorentz integral transform (LIT) is
provided together with the spectrum of the LIT kernel. The exponential increase
of the inverse Fourier transform of the LIT kernel entering the inversion
formula explains the ill-posed character of the LIT approach. Also the
continuous spectrum of the LIT kernel, which approaches zero points necessarily
to the same defect. A possible cure is discussed and numerically illustrated.
