Ukrainian Mathematical Journal

, Volume 67, Issue 9, pp 1336–1348 | Cite as

One Problem Connected with the Helgason Support Problem

  • V. V. Volchkov
  • Vit. V. Volchkov
  • I. N. Savost’yanova

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.


Symmetric Space Hyperbolic Space Legendre Function Annular Region Integral Geometry 
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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • V. V. Volchkov
    • 1
  • Vit. V. Volchkov
    • 1
  • I. N. Savost’yanova
    • 1
  1. 1.Donetsk National UniversityDonetskUkraine

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