Geodesic
An underdetermined problem of integral geometry for the generalized Radon transform
Sibirskij žurnal industrialʹnoj matematiki, Tome 19 (2016) no. 1, pp. 18-26

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Under study is some new problem of integral geometry. All planes are considered in the three-dimensional Euclidean space. The data are given by the integrals over all such planes of an unknown piecewise-smooth function depending both on the spatial variables and the variables characterizing the planes. The sought object is an integrant discontinuity surface of the first kind. The uniquiness theorem of of the desired surface is proved. The research od the papert presents an aspects of the theory of probing an unknown medium by various physical signals.
Keywords: integral geometry, generalized Radon transform, probing, unknown boundaries. 
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     author = {D. S. Anikonov and Ya. A. Kipriyanov},
     title = {An underdetermined problem of integral geometry for the generalized {Radon} transform},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {18--26},
     publisher = {mathdoc},
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     number = {1},
     year = {2016},
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     url = {http://geodesic.mathdoc.fr/item/SJIM_2016_19_1_a1/}
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D. S. Anikonov; Ya. A. Kipriyanov. An underdetermined problem of integral geometry for the generalized Radon transform. Sibirskij žurnal industrialʹnoj matematiki, Tome 19 (2016) no. 1, pp. 18-26. http://geodesic.mathdoc.fr/item/SJIM_2016_19_1_a1/