Geodesic
Injectivity sets for the Radon transform over a~sphere
Izvestiya. Mathematics , Tome 63 (1999) no. 3, pp. 481-493

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This paper contains a solution of the problem of describing the kernel of the Radon transform over a sphere with respect to sets with spherical symmetry. This solution enabled us, in particular, to characterize all injectivity sets of this type. The technique used in the proofs enabled us to obtain other exact results concerning spherical means, namely, new two-radii theorems and a uniqueness theorem. 
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     author = {V. V. Volchkov},
     title = {Injectivity sets for the {Radon} transform over a~sphere},
     journal = {Izvestiya. Mathematics },
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     url = {http://geodesic.mathdoc.fr/item/IM2_1999_63_3_a1/}
}
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V. V. Volchkov. Injectivity sets for the Radon transform over a~sphere. Izvestiya. Mathematics , Tome 63 (1999) no. 3, pp. 481-493. http://geodesic.mathdoc.fr/item/IM2_1999_63_3_a1/