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arXiv · 2102.09279

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

Teppo Mertens·Frank Sommen
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Abstract

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.

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Teppo Mertens, Frank Sommen. 2021-02-18. Inversions for the Hua-Radon and the polarized Hua-Radon transform. https://arxiv.org/abs/2102.09279

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