2017
Том 69
№ 6

All Issues

One Problem Connected with the Helgason Support Problem

Savost’yanova I. M., Volchkov V. V., Volchkov V. V.


Abstract

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.