On the Range of the Radon d-Plane Transform and Its Dual

DOI10.2307/2001816zbMath0743.44002OpenAlexW4233355508MaRDI QIDQ3982154

Fulton B. Gonzalez

Publication date: 26 June 1992

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

Full work available at URL: https://doi.org/10.2307/2001816

zbMATH Keywords

counterexampleEuclidean motion groupmoment conditionsdual Radon transformaffine Grassmann manifoldrange theoreminfinitesimal left regular representationRadon \(d\)-plane transform

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Radon transform (44A12) Integration on manifolds; measures on manifolds (58C35) Integral geometry (53C65)

Related Items (8)

Moment conditions and support theorems for Radon transforms on affine Grassmann manifolds ⋮ Reconstruction of functions from their integrals over \(k\)-planes ⋮ Range characterization of Radon transforms on quaternionic projective spaces ⋮ Invariant differential operators and the range of the matrix Radon transform ⋮ Integral geometry on Grassmann manifolds and calculus of invariant differential operators ⋮ Unique continuation property and Poincaré inequality for higher order fractional Laplacians with applications in inverse problems ⋮ Inversion of \(k\)-plane transforms via continuous wavelet transforms ⋮ The Calderón reproducing formula, windowed \(X\)-ray transforms, and Radon transforms in \(L^p\)-spaces

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