  It is shown that dynamical equations for quantum tomograms retain the
normalization conditions of their solutions during evolution only if the
solutions satisfy a set of special conditions. These conditions are found
explicitly. On the contrary, it is also shown that the classical Liouville
equation, Moyal equation for Wigner function, and evolution equation for Husimi
function retain normalization of any initially normalized and quickly decaying
at infinity functions on the phase space. Other necessary and sufficient
conditions for optical and symplectic tomogram-like functions to be tomograms
of physical states are discussed.
