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The monogenic Hua–Radon transform and its inverse

Denis Constales (UGent) , Hendrik De Bie (UGent) , Teppo Mertens (UGent) and Franciscus Sommen (UGent)
(2022) JOURNAL OF GEOMETRIC ANALYSIS. 32(1).
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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 29:2709-2737, 2019), 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.
Keywords
Holomorphic functions, Monogenic functions, Lie ball, Lie sphere, Radon-type transforms

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MLA
Constales, Denis, et al. “The Monogenic Hua–Radon Transform and Its Inverse.” JOURNAL OF GEOMETRIC ANALYSIS, vol. 32, no. 1, 2022, doi:10.1007/s12220-021-00749-3.
APA
Constales, D., De Bie, H., Mertens, T., & Sommen, F. (2022). The monogenic Hua–Radon transform and its inverse. JOURNAL OF GEOMETRIC ANALYSIS, 32(1). https://doi.org/10.1007/s12220-021-00749-3
Chicago author-date
Constales, Denis, Hendrik De Bie, Teppo Mertens, and Franciscus Sommen. 2022. “The Monogenic Hua–Radon Transform and Its Inverse.” JOURNAL OF GEOMETRIC ANALYSIS 32 (1). https://doi.org/10.1007/s12220-021-00749-3.
Chicago author-date (all authors)
Constales, Denis, Hendrik De Bie, Teppo Mertens, and Franciscus Sommen. 2022. “The Monogenic Hua–Radon Transform and Its Inverse.” JOURNAL OF GEOMETRIC ANALYSIS 32 (1). doi:10.1007/s12220-021-00749-3.
Vancouver
1.
Constales D, De Bie H, Mertens T, Sommen F. The monogenic Hua–Radon transform and its inverse. JOURNAL OF GEOMETRIC ANALYSIS. 2022;32(1).
IEEE
[1]
D. Constales, H. De Bie, T. Mertens, and F. Sommen, “The monogenic Hua–Radon transform and its inverse,” JOURNAL OF GEOMETRIC ANALYSIS, vol. 32, no. 1, 2022.
@article{8756853,
  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 29:2709-2737, 2019), 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.}},
  articleno    = {{16}},
  author       = {{Constales, Denis and De Bie, Hendrik and Mertens, Teppo and Sommen, Franciscus}},
  issn         = {{1050-6926}},
  journal      = {{JOURNAL OF GEOMETRIC ANALYSIS}},
  keywords     = {{Holomorphic functions,Monogenic functions,Lie ball,Lie sphere,Radon-type transforms}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{38}},
  title        = {{The monogenic Hua–Radon transform and its inverse}},
  url          = {{http://doi.org/10.1007/s12220-021-00749-3}},
  volume       = {{32}},
  year         = {{2022}},
}
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