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Extremal cases of the Pompeiu problem

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Abstract

The Pompeiu problem is studied for functions defined on a ballB ⊂ ℝn and having zero integrals over all sets congruent to a given compact setK ⊂B. The problem of finding the least radiusr=r(K) ofB for whichK is a Pompeiu set is considered. The solution is obtained for the cases in whichK is a cube or a hemisphere.

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Authors and Affiliations

  1. Donetsk State University, USSR

    V. V. Volchkov

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  1. V. V. Volchkov
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Translated fromMatematicheskie Zametki, Vol. 59, No. 5, pp. 671–680, May, 1996.

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Volchkov, V.V. Extremal cases of the Pompeiu problem. Math Notes 59, 482–489 (1996). https://doi.org/10.1007/BF02308814

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  • DOI: https://doi.org/10.1007/BF02308814

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