On the Pompeiu problem and its generalizations
Functions are investigated whose integrals over a given collection of sets are zero. Pompeiu sets are described in terms of the approximation of their indicators by linear combinations of the indicators of balls with special radii.
English version (Springer): Ukrainian Mathematical Journal 45 (1993), no. 10, pp 1623-1628.
Citation Example: Volchkov V. V. On the Pompeiu problem and its generalizations // Ukr. Mat. Zh. - 1993. - 45, № 10. - pp. 1444–1448.