Helgason-Marchaud inversion formulas for Radon transforms

DOI10.1090/S0002-9939-02-06554-1zbMath1002.44001OpenAlexW1908298474MaRDI QIDQ4536065

Boris Rubin

Publication date: 17 June 2002

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-02-06554-1

zbMATH Keywords

hyperbolic spaceMarchaud's fractional derivativesgeodesic Radon transformsHelgason-Marchaud inversion formulas

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Radon transform (44A12) Integral geometry (53C65) Random convex sets and integral geometry (aspects of convex geometry) (52A22)

Related Items (9)

Reconstruction of functions from their integrals over \(k\)-planes ⋮ Lower bounds for ranks of elliptic curves ⋮ On a Radon Transform ⋮ New inversion formulas for the horospherical transform ⋮ A nonsplit sum of coefficients of modular forms ⋮ Radon transforms over lower-dimensional horospheres in real hyperbolic space ⋮ Inversion formulas of integral geometry in real hyperbolic space ⋮ A generalization of the Mader-Helgason inversion formulas for Radon transforms ⋮ Inversion formulas for the spherical Radon transform and the generalized cosine transform.

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(L^ p\) estimates for Radon transforms in Euclidean and non-Euclidean spaces
• Spherical Radon transform and related wavelet transforms
• The Radon transform.
• Inversion formulas for the \(k\)-dimensional Radon transform in real hyperbolic spaces
• Radon, cosine and sine transforms on real hyperbolic space
• Inversion formulas for the spherical Radon transform and the generalized cosine transform.
• Differential operators on homogeneous spaces
• Radon transform of Lp -functions on the Lobachevsky space and hyperbolic wavelet transforms

This page was built for publication: Helgason-Marchaud inversion formulas for Radon transforms