  The singular value decomposition going with many problems in medical imaging,
non-destructive testing, geophysics, is of central importance. Unfortunately
the effective numerical determination of the singular functions in question is
a very ill-posed problem. The best known remedy to this problem goes back to
the work of D. Slepian, H.Landau and H. Pollak, Bell Labs 1960-1965. We show
that the master symmetries of the Korteweg-de Vries equation give a way to
extend the remarkable result of D. Slepian in connection with the Bessel
integral kernel and the existence of a differential operator that commutes with
the corresponding integral operator. The original results of the Bell Labs
group has already played an important role in the study of the limited angle
problem in X-ray tomography as well as in Random Matrix theory.
