Geodesic
Determination of compact subsets from functionals on them
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 2 (2005), pp. 167-185

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The problems of determination of convex bodies and non-convex analytical manifolds in $R^n$ from projections, curvature integrals, sections and measures of sections of its polar are considered. 
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     author = {V. N. Stepanov},
     title = {Determination of compact subsets from functionals on them},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {167--185},
     publisher = {mathdoc},
     volume = {2},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2005_2_a11/}
}
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V. N. Stepanov. Determination of compact subsets from functionals on them. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 2 (2005), pp. 167-185. http://geodesic.mathdoc.fr/item/SEMR_2005_2_a11/