2021/02/18 by Teppo Mertens, Mertens, Teppo, Frank Sommen +1
Mathematics · #30G35 #32A50 #44A12 #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #math.CA #math.CV #msc:30G35 #msc:32A50 #msc:44A12
paper · pdf · doi:10.48550/arxiv.2102.09279
22 pages, minor changes and references added
arxiv created 2021/05/06 · arxiv updated 2021/05/07
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.