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<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^{2}(\mathbb {R}^{n})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>L</mi> <mn>2</mn> </msup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>n</mi> </msup> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> 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.</p>

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Radon-Type Transforms for Holomorphic and Hermitian Monogenic Functions

  • 期刊论文

  • 发表日期：

    2026年5月28日

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  • Ren Hu,
  • Pan Lian

摘要

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 \(L^{2}(\mathbb {R}^{n})\) L 2 ( 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.