New Inversion Formulas for the Horospherical Transform

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• 作者：Boris Rubin
• 关键词：Real hyperbolic space ; Horospherical transform ; Radon transform ; Inversion formulas ; \(L^p\) ; Spaces
• 刊名：The Journal of Geometric Analysis
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：27
• 期：1
• 页码：908-946
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Differential Geometry; Convex and Discrete Geometry; Fourier Analysis; Abstract Harmonic Analysis; Dynamical Systems and Ergodic Theory; Global Analysis and Analysis on Manifolds;
• 出版者：Springer US
• ISSN：1559-002X
• 卷排序：27

文摘

The following two inversion methods for totally geodesic Radon transforms on constant curvature spaces are well known in integral geometry. The first method employs mean value operators in accordance with the classical Funk–Radon–Helgason scheme. The second one relies on the properties of potentials that can be inverted by polynomials of the Beltrami–Laplace operator. Using tools of harmonic analysis, we show that both methods are also applicable to the horospherical transform on the real hyperbolic space.