Geodesic
Approximation of the absorption coefficient for the radiative transfer equation on a~given energy interval
Sibirskij žurnal industrialʹnoj matematiki, Tome 7 (2004) no. 4, pp. 116-129

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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. 
@article{SJIM_2004_7_4_a10,
     author = {V. G. Nazarov},
     title = {Approximation of the absorption coefficient for the radiative transfer equation on a~given energy interval},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {116--129},
     publisher = {mathdoc},
     volume = {7},
     number = {4},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2004_7_4_a10/}
}
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V. G. Nazarov. Approximation of the absorption coefficient for the radiative transfer equation on a~given energy interval. Sibirskij žurnal industrialʹnoj matematiki, Tome 7 (2004) no. 4, pp. 116-129. http://geodesic.mathdoc.fr/item/SJIM_2004_7_4_a10/