The monogenic Hua-Radon transform and its inverse

Inversions for the Hua-Radon and the polarized Hua-Radon transform

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.

全纯与 Hermitian 单演函数的 Radon 型变换

Radon-type transforms for holomorphic and Hermitian monogenic functions

本文针对单位球上的调和、全纯及 Hermitian 单演函数，引入余维数为 2 的 Radon 型变换，基于对偶变换导出反演公式，并推广至 Fock 空间与 L²(Rⁿ)，细化了 Szegö-Radon 变换。