Geodesic
Extremal cases of the Pompeiu problem
Matematičeskie zametki, Tome 59 (1996) no. 5, pp. 671-680

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The Pompeiu problem is studied for functions defined on a ball $B\subset\mathbb R^n$ and having zero integrals over all sets congruent to a given compact set $K\subset B$. The problem of finding the least radius $r=r(K)$ of $B$ for which $K$ is a Pompeiu set is considered. The solution is obtained for the cases in which $K$ is a cube or a hemisphere. 
@article{MZM_1996_59_5_a2,
     author = {V. V. Volchkov},
     title = {Extremal cases of the {Pompeiu} problem},
     journal = {Matemati\v{c}eskie zametki},
     pages = {671--680},
     publisher = {mathdoc},
     volume = {59},
     number = {5},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1996_59_5_a2/}
}
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V. V. Volchkov. Extremal cases of the Pompeiu problem. Matematičeskie zametki, Tome 59 (1996) no. 5, pp. 671-680. http://geodesic.mathdoc.fr/item/MZM_1996_59_5_a2/