Journal d'Analyse Mathématique

, Volume 128, Issue 1, pp 191–214 | Cite as

Range description for a spherical mean transform on spaces of constant curvature

  • Linh V. Nguyen


Let X be a Riemannian manifold and R be the spherical mean transform in X. Let S be a geodesic sphere in X and R S be the restriction of R to the set of geodesic spheres centered on S. We present a complete range description for R S when X is either the hyperbolic space H n or the sphere S n (n ≥ 2 in both cases). The description is analogous to a result for the euclidean space ℝ n obtained by M. Agranovsky, D. Finch, and P. Kuchment and by M. Agranovsky and L. V. Nguyen.


Inverse Problem Riemannian Manifold Hyperbolic Space Constant Curvature Orthogonality Condition 
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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© Hebrew University Magnes Press 2016

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of IdahoMoscowUSA

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