Solution of the Inverse Problem of the Transfer of Ultrarelativistic Nuclei in the Expanding Universe

We consider propagation of nuclei with energies over 1018 eV in the expanding Universe filled with background electromagnetic radiation. The spectrum of sources of extragalactic cosmic rays for protons and nuclei up to iron is determined on the basis of the particle spectrum observed near Earth as a solution of the inverse problem of transfer of ultrarelativistic nuclei. The method of regularization of the solution of this mathematically ill-posed problem is used basing on the data of the Pierre Auger Observatory on the energy spectrum of cosmic rays, the average logarithm of the mass number, and its variance. The found energy spectra of the sources prove to be very hard and strongly dependent on the assumption about the composition of the accelerated nuclei.