The monogenic Hua-Radon transform and its inverse

2020/11/23 by Denis Constales, Constales, Denis, Hendrik De Bie +5
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA

paper · pdf · doi:10.48550/arxiv.2011.11457

30 pages, minor revisions added

arxiv created 2021/08/19 · arxiv updated 2021/08/20

Abstract

The monogenic Hua-Radon transform is defined as an orthogonal projection on holomorphic functions in the Lie sphere. Extending the work of Sabadini and Sommen, J. Geom. Anal. 29 (2019), 2709-2737, we determine its reproducing kernel. Integrating this kernel over the Stiefel manifold yields a linear combination of the zonal spherical monogenics. Using the reproducing properties of those monogenics we obtain an inversion for the monogenic Hua-Radon transform.

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