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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 9, pp. 1189–1200, September, 2015.
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Volchkov, V.V., Volchkov, V.V. & Savost’yanova, I.N. One Problem Connected with the Helgason Support Problem. Ukr Math J 67, 1336–1348 (2016). https://doi.org/10.1007/s11253-016-1157-x
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DOI: https://doi.org/10.1007/s11253-016-1157-x