Commuting integral and differential operators and the master symmetries of the Korteweg–de Vries equation

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