Radon-type transforms for holomorphic functions in the lie ball
- Author
- Irene Sabadini and Franciscus Sommen (UGent)
- Organization
- Abstract
- In this paper, we consider holomorphic functions on the m-dimensional Lie ball LB(0,1) which admit a square integrable extension on the Lie sphere. We then define orthogonal projections of this set onto suitable subsets of functions defined in lower- dimensional spaces to obtain several Radon-type transforms. For all these transforms we provide the kernel and an integral representation, besides other properties. In particular, we introduce and study a generalization to the Lie ball of the Szeg-Radon transform introduced in Colombo et al. (Adv Appl Math 74:1-22, 2016), and various types of Hua-Radon transforms.
- Keywords
- Holomorphic functions, Monogenic functions, Lie ball, Lie sphere, Radon-type transforms
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8635436
- MLA
- Sabadini, Irene, and Franciscus Sommen. “Radon-Type Transforms for Holomorphic Functions in the Lie Ball.” JOURNAL OF GEOMETRIC ANALYSIS, vol. 29, no. 3, 2019, pp. 2709–37, doi:10.1007/s12220-018-0090-7.
- APA
- Sabadini, I., & Sommen, F. (2019). Radon-type transforms for holomorphic functions in the lie ball. JOURNAL OF GEOMETRIC ANALYSIS, 29(3), 2709–2737. https://doi.org/10.1007/s12220-018-0090-7
- Chicago author-date
- Sabadini, Irene, and Franciscus Sommen. 2019. “Radon-Type Transforms for Holomorphic Functions in the Lie Ball.” JOURNAL OF GEOMETRIC ANALYSIS 29 (3): 2709–37. https://doi.org/10.1007/s12220-018-0090-7.
- Chicago author-date (all authors)
- Sabadini, Irene, and Franciscus Sommen. 2019. “Radon-Type Transforms for Holomorphic Functions in the Lie Ball.” JOURNAL OF GEOMETRIC ANALYSIS 29 (3): 2709–2737. doi:10.1007/s12220-018-0090-7.
- Vancouver
- 1.Sabadini I, Sommen F. Radon-type transforms for holomorphic functions in the lie ball. JOURNAL OF GEOMETRIC ANALYSIS. 2019;29(3):2709–37.
- IEEE
- [1]I. Sabadini and F. Sommen, “Radon-type transforms for holomorphic functions in the lie ball,” JOURNAL OF GEOMETRIC ANALYSIS, vol. 29, no. 3, pp. 2709–2737, 2019.
@article{8635436,
abstract = {{In this paper, we consider holomorphic functions on the m-dimensional Lie ball LB(0,1) which admit a square integrable extension on the Lie sphere. We then define orthogonal projections of this set onto suitable subsets of functions defined in lower- dimensional spaces to obtain several Radon-type transforms. For all these transforms we provide the kernel and an integral representation, besides other properties. In particular, we introduce and study a generalization to the Lie ball of the Szeg-Radon transform introduced in Colombo et al. (Adv Appl Math 74:1-22, 2016), and various types of Hua-Radon transforms.}},
author = {{Sabadini, Irene 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 = {{3}},
pages = {{2709--2737}},
title = {{Radon-type transforms for holomorphic functions in the lie ball}},
url = {{http://doi.org/10.1007/s12220-018-0090-7}},
volume = {{29}},
year = {{2019}},
}
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