Abstract
The k-dimensional totally geodesic Radon transform on the unit sphere Sn and the corresponding cosine transform can be regarded as members of the analytic family of intertwining fractional integrals Rαf(ξ)=γn,k(α)∫Snf(x)sind(x,ξ)α+k−ndx,d(x,ξ) being the geodesic distance between x∈Sn and the k-geodesic ξ. We develop a unified approach to the inversion of Rαf for all α⩾0,1⩽k⩽n−1,n⩾2. The cases of smooth f and f∈Lp are considered. A series of new inversion formulas is obtained. The convolution–backprojection method is developed.
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