Approximation of the absorption coefficient for the radiative transfer equation on a given energy interval

We consider the approximation of the absorption coefficient of the energy of a given substance for the radiative transfer equation by the absorption coefficient of a mixture of other substances on some energy interval. We indicate a connection between this problem and the problem of determining the internal structure of a nonhomogeneous medium from the results of its tomographic sounding. We give a geometric interpretation of the problem and its solution. For a given energy grid, we obtain necessary and sufficient conditions for the best approximation of the absorption coefficient.