Radon-type transforms for holomorphic and Hermitian monogenic functions
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911143234109440 |
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| author | Hu, Ren Lian, Pan |
| author_facet | Hu, Ren Lian, Pan |
| contents | The standard Radon transform of holomorphic functions is not always well defined, as the integration of such functions over planes may not converge. In this paper, we introduce new Radon-type transforms of co-(real)dimension $2$ for harmonic and holomorphic functions on the unit ball. These transforms are abstractly defined as orthogonal projections onto spaces of complex harmonic and holomorphic plane waves, respectively. The inversion formulas are derived based on the dual transform, while the latter is defined as an integration on a complex Stiefel manifold. Our transforms are extended to the Fock space and give rise to a new transform defined on the entire $L^{2}(\mathbb{R}^{n})$ through the Segal-Bargmann transform. Furthermore, we develop these transforms for Hermitian monogenic functions on the unit ball, thereby refining the Szegö-Radon transform for monogenic functions introduced by Colombo, Sabadini and Sommen. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00745 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Radon-type transforms for holomorphic and Hermitian monogenic functions Hu, Ren Lian, Pan Complex Variables Classical Analysis and ODEs 30G35 The standard Radon transform of holomorphic functions is not always well defined, as the integration of such functions over planes may not converge. In this paper, we introduce new Radon-type transforms of co-(real)dimension $2$ for harmonic and holomorphic functions on the unit ball. These transforms are abstractly defined as orthogonal projections onto spaces of complex harmonic and holomorphic plane waves, respectively. The inversion formulas are derived based on the dual transform, while the latter is defined as an integration on a complex Stiefel manifold. Our transforms are extended to the Fock space and give rise to a new transform defined on the entire $L^{2}(\mathbb{R}^{n})$ through the Segal-Bargmann transform. Furthermore, we develop these transforms for Hermitian monogenic functions on the unit ball, thereby refining the Szegö-Radon transform for monogenic functions introduced by Colombo, Sabadini and Sommen. |
| title | Radon-type transforms for holomorphic and Hermitian monogenic functions |
| topic | Complex Variables Classical Analysis and ODEs 30G35 |
| url | https://arxiv.org/abs/2401.00745 |