TY - JOUR AU - V. V. Volchkov AU - V. V. Volchkov AU - I. M. Savost’yanova PY - 2015/09/25 Y2 - 2024/03/29 TI - One Problem Connected with the Helgason Support Problem JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 67 IS - 9 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2058 AB - 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. ER -