We consider tomograms and quasidistributions, such as the Wigner functions, the Glauber–Sudarshan Pfunctions,
and the Husimi Q-functions, that violate the standard normalization condition for probability
distribution fucntions. We introduce special conditions for the Wigner function to determine the tomogram
with the Radon transform and study three different examples of states like the de Broglie plane wave, the
Moschinsky shutter problem, and the stationary state of a charged particle in a uniform constant electric
field. We show that their tomograms and quasidistribution functions expressed in terms of the Dirac delta
function, the Airy function, and Fresnel integrals violate the standard normalization condition and the
density matrix of the state therefore cannot always be reconstructed. We propose a method that allows
circumventing this problem using a special tomogram in the limit form.