One Problem Connected with the Helgason Support Problem
We solve the problem of description of the set of continuous functions in annular subdomains of the n-dimensional sphere with zero integrals over all (n - 1)-dimensional spheres covering the inner spherical cap. As an application, we establish a spherical analog of the Helgason support theorem and new uniqueness theorems for functions with zero spherical means.
English version (Springer): Ukrainian Mathematical Journal 67 (2015), no. 9, pp 1336-1348.
Citation Example: Savost’yanova I. M., Volchkov V. V., Volchkov V. V. One Problem Connected with the Helgason Support Problem // Ukr. Mat. Zh. - 2015. - 67, № 9. - pp. 1189-1200.