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

Teppo Mertens and Frank Sommen

Applied Mathematics and Computation, 2021, vol. 411, issue C

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.

Keywords: Holomorphic functions; Monogenic functions; Lie ball; Lie sphere; Radon-type transforms (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:411:y:2021:i:c:s0096300321006147

DOI: 10.1016/j.amc.2021.126525

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