One Problem Connected with the Helgason Support Problem - Volchkov, V. V.; Volchkov, V. V.; Savost’yanova, I. M. (Ukrains’kyi Matematychnyi Zhurnal, 2015)
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.