We obtain new conditions for the injectivity of the Pompeiu transformation for integral ball means are obtained. The main results substantially improve some known uniqueness theorems for functions with vanishing integrals over balls of fixed radius.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 12, pp. 1676–1684, December, 2012.
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Ochakovskaya, O.A. Injectivity Classes of the Pompeiu Transformation. Ukr Math J 64, 1893–1902 (2013). https://doi.org/10.1007/s11253-013-0758-x
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DOI: https://doi.org/10.1007/s11253-013-0758-x