The known integral transforms of Funk–Radon type are applied to manifolds which have algebraic structure (planes, spheres, ellipsoids, hyperboloids etc.). A variety of new exact reconstructions is described in this paper for integral transforms of Funk–Radon type on smooth hypersurfaces Xn properly embedded in space Rn+1 which is endowed with an additional structure.

中文翻译：

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从非解析流形上的积分重建

已知的 Funk-Radon 类型的积分变换应用于具有代数结构（平面、球体、椭圆体、双曲面等）的流形。本文描述了各种新的精确重建，用于平滑超曲面上的 Funk-Radon 类型的积分变换Xn正确嵌入空间Rn+1它被赋予了额外的结构。