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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
Article
  • 39 Downloads

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.

Keywords

Symmetric Space Hyperbolic Space Legendre Function Annular Region Integral Geometry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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