The Hua-Radon and polarized Hua-Radon transform are two orthogonal projections defined on holomorphic functions in the Lie sphere. Both transformations can be written as integral transforms with respect to a suitable reproducing kernel. Integrating both kernels over a Stiefel manifold yields a linear combination of zonal spherical monogenics. Using an Almansi type decomposition of holomorphic functions and reproducing properties of the zonal monogenics, we obtain an inversion formula for both the Hua-Radon and the polarized Hua-Radon transform.

中文翻译：

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Hua-Radon 和极化 Hua-Radon 变换的反演

Hua-Radon 和极化 Hua-Radon 变换是定义在李球面全纯函数上的两个正交投影。两种变换都可以写成相对于合适的再现内核的积分变换。在 Stiefel 流形上对两个核进行积分会产生带状球形单基因的线性组合。利用全纯函数的 Almansi 型分解和纬向单基因的再现特性，我们获得了华-氡和极化的华-氡变换的反演公式。