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