Sur la transformation de Radon de la sphère $S\sp d$

DOI10.24033/bsmf.2212zbMath0798.44002OpenAlexW2522405979MaRDI QIDQ4282757

Radouan Daher, Ahmed Abouelaz

Publication date: 11 April 1994

Published in: Bulletin de la Société mathématique de France (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=BSMF_1993__121_3_353_0

zbMATH Keywords

inversion formulaPlancherel formuladual Radon transformLaplace-Beltrami-OperatorRadon transform on the sphere

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Radon transform (44A12) Analysis on real and complex Lie groups (22E30) Harmonic analysis and spherical functions (43A90)

Related Items (15)

Funk-Minkowski transform and spherical convolution of Hilbert type in reconstructing functions on the sphere ⋮ Support theorems for Funk-type isodistant Radon transforms on constant curvature spaces ⋮ An SVD in Spherical Surface Wave Tomography ⋮ On the spherical slice transform ⋮ Radon transforms and Gegenbauer-Chebyshev integrals. II: Examples ⋮ Sliced optimal transport on the sphere ⋮ Non-central Funk-Radon transforms: single and multiple ⋮ The Funk-Radon transform for hyperplane sections through a common point ⋮ On two families of Funk-type transforms ⋮ A generalization of the Funk–Radon transform ⋮ Reconstruction of functions on the sphere from their integrals over hyperplane sections ⋮ Spherical Radon transform and related wavelet transforms ⋮ Integral geometry on discrete Grassmannians in \(\mathbb{Z}^n\) ⋮ The \(d\)-plane Radon transform on the torus \(\mathbb T^n\) ⋮ Holomorphic extension associated with Fourier-Legendre expansions

Cites Work

• Transformation intégrale de Weyl et théorème de Paley-Wiener associes à un opérateur différentiel singulier sur \((0,\infty)\)
• The Fourier transform of Harish-Chandra's \(c\)-function and inversion of the Abel transform
• \(L^ p\) estimates for Radon transforms in Euclidean and non-Euclidean spaces
• A new proof of a Paley-Wiener type theorem for the Jacobi transform
• The Radon transform on Euclidean spaces, compact two-point homogeneous spaces and Grassmann manifolds
• A duality for symmetric spaces with applications to group representations
• Fourier Analysis on the Sphere
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