A note on k-plane integral transforms

DOI10.1016/0022-247X(79)90196-3zbMath0416.44003OpenAlexW80418025MaRDI QIDQ754432

Donald C. Solmon

Publication date: 1979

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-247x(79)90196-3

zbMATH Keywords

integral transformsa priori inequalitiesmapping properties

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Pseudodifferential and Fourier integral operators on manifolds (58J40)

Related Items (19)

Asymptotic formulas for the dual Radon transform and applications ⋮ Analytic Multipliers of the Radon Transform ⋮ Reconstruction of functions from their integrals over \(k\)-planes ⋮ Radon transforms on affine Grassmannians ⋮ Weighted norm inequalities for $k$-plane transforms ⋮ Fourier and Radon transform on harmonic 𝑁𝐴 groups ⋮ On some inversion formulas for Riesz potentials and k-plane transforms ⋮ The \(k\)-plane transform on the Heisenberg group ⋮ Norm estimates for \(k\)-plane transforms and geometric inequalities ⋮ METHOD OF MEAN VALUE OPERATORS FOR RADON TRANSFORMS IN THE SPACE OF MATRICES ⋮ 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 ⋮ Weighted estimates for the \(k\)-plane transform of radial functions on Euclidean spaces ⋮ Continuity properties of k-plane integrals and Besicovitch sets ⋮ Inversion of \(k\)-plane transforms via continuous wavelet transforms ⋮ The Calderón reproducing formula, windowed \(X\)-ray transforms, and Radon transforms in \(L^p\)-spaces ⋮ Convolution-backprojection method for the \(k\)-plane transform, and Calderón's identity for ridgelet transforms ⋮ Sharp endpoint estimates for the $X$-ray transform and the Radon transform in finite fields ⋮ Derivative norm estimates for the radon transform with application to tomography

Cites Work

• Unnamed Item
• The spaces \(L^ p\), with mixed norm
• Lower dimensional integrability of \(L^2\) functions
• The X-ray transform
• The Radon transform on Euclidean spaces, compact two-point homogeneous spaces and Grassmann manifolds
• Practical and mathematical aspects of the problem of reconstructing objects from radiographs
• Uniform asymptotic expansions at a caustic

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