Radon, cosine and sine transforms on real hyperbolic space

DOI10.1006/aima.2002.2074zbMath1013.43006OpenAlexW2078300961MaRDI QIDQ1851238

Boris Rubin

Publication date: 16 December 2002

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/aima.2002.2074

zbMATH Keywords

Radon transformLaplace-Beltrami operatorinversion formulaehyperbolic cosine and sine transformsintertwining fractional integrals

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85)

Related Items (17)

Radon transform on real, complex, and quaternionic Grassmannians ⋮ Reconstruction of functions from their integrals over \(k\)-planes ⋮ Helgason-Marchaud inversion formulas for Radon transforms ⋮ A stereoscopic look into the bulk ⋮ On the sine polarity and the \(L_p\)-sine Blaschke-Santaló inequality ⋮ Higher-rank Radon transforms on constant curvature spaces ⋮ The Radon transform on the Heisenberg group and the transversal Radon transform ⋮ End point estimates for Radon transform of radial functions on non-Euclidean spaces ⋮ Semyanistyi's integrals and Radon transforms on matrix spaces ⋮ New inversion formulas for the horospherical transform ⋮ Reconstruction of functions on the sphere from their integrals over hyperplane sections ⋮ Radon transform on symmetric matrix domains ⋮ Radon transforms over lower-dimensional horospheres in real hyperbolic space ⋮ Convolution-backprojection method for the \(k\)-plane transform, and Calderón's identity for ridgelet transforms ⋮ Inversion formulas of integral geometry in real hyperbolic space ⋮ X-ray transform on a symmetric space ⋮ Inversion formulas for the spherical Radon transform and the generalized cosine transform.

Cites Work

• \(L^ p\) estimates for Radon transforms in Euclidean and non-Euclidean spaces
• The Radon transform on hyperbolic space
• Sharp estimates for some functions of the Laplacian on noncompact symmetric spaces
• The Radon transform.
• The range characterizations of the totally geodesic Radon transform on the real hyperbolic space
• Inversion formulas for the \(k\)-dimensional Radon transform in real hyperbolic spaces
• Inversion formulas for the spherical Radon transform and the generalized cosine transform.
• Differential operators on homogeneous spaces
• The convolution structure for Jacobi function expansions
• Range of the k-dimensional Radon transform in real hyperbolic spaces
• Support Theorems for Totally Geodesic Radon Transforms on Constant Curvature Spaces
• Radon transform of Lp -functions on the Lobachevsky space and hyperbolic wavelet transforms
• The Invertibility of the Radon Transform on Abstract Rotational Manifolds of Real Type.
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