We obtain explicit inversion formulas for the Radon-like transform that assigns to a function on the unit sphere the integrals of that function over hemispheres lying in lower dimensional central cross-sections. The results are applied to determination of star bodies from the volumes of their central half-sections.
Generalized cosine transforms and classes of star bodies
On the Determination of a Function from an Elliptical Radon Transform
On the determination of a function from its cone transform with fixed central axis
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