A uniqueness theorem is proved for functions defined in \( {{\mathbb R}^n}, \; {n \geq 2} \), with vanishing integrals over the balls of fixed radius and a given majorant of growth. The problem of unimprovability of this theorem is analyzed.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 3, pp. 361–368, March, 2011.
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Ochakovskaya, O.A. On the injectivity of the Pompeiu transform for integral ball means. Ukr Math J 63, 416–424 (2011). https://doi.org/10.1007/s11253-011-0512-1
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DOI: https://doi.org/10.1007/s11253-011-0512-1