Integral geometry on Grassmann manifolds and calculus of invariant differential operators

DOI10.1006/jfan.1999.3459zbMath0976.53081OpenAlexW1999698361MaRDI QIDQ1125280

Tomoyuki Kakehi

Publication date: 18 December 2001

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jfan.1999.3459

zbMATH Keywords

Radon transforminversion formulaGrassmann manifoldintegral geometryinvariant differential operatorradial parteigenvalue formularange-characterization

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Radon transform (44A12) Integral geometry (53C65)

Related Items (18)

Injectivity of the Heisenberg X-ray transform ⋮ Moment conditions and support theorems for Radon transforms on affine Grassmann manifolds ⋮ Radon transform on real, complex, and quaternionic Grassmannians ⋮ Dual Radon transforms on affine Grassmann manifolds ⋮ Funk, cosine, and sine transforms on Stiefel and Grassmann manifolds ⋮ Range theorems and inversion formulas for Radon transforms on Grassmann manifolds ⋮ On Radon transforms between lines and hyperplanes ⋮ Quasianalyticity, uncertainty, and integral transforms on higher Grassmannians ⋮ Higher-rank Radon transforms on constant curvature spaces ⋮ Radon transforms for quasi-equivariant \(\mathcal D\)-modules on generalized flag manifolds ⋮ METHOD OF MEAN VALUE OPERATORS FOR RADON TRANSFORMS IN THE SPACE OF MATRICES ⋮ On an αth-order fractional Radon transform and a wave type of equation ⋮ Functional Relations, Sharp Mapping Properties, and Regularization of the X-Ray Transform on Disks of Constant Curvature ⋮ The \(\lambda \)-cosine transforms, differential operators, and Funk transforms on Stiefel and Grassmann manifolds ⋮ Radon transforms of constructible functions on Grassmann manifolds ⋮ Radon transform on symmetric matrix domains ⋮ The Radon transform for double fibrations of semisimple symmetric spaces ⋮ Book Review: Integral geometry and Radon transforms

Cites Work

• On the range of the Radon transform and its dual
• Radon transforms on higher rank Grassmannians
• On images of Radon transforms
• Invariant differential operators and the range of the Radon d-plane transform
• The Radon transform
• Integral geometry in affine and projective spaces
• Spherical functions and invariant differential operators on complex Grassmann manifolds
• Range characterization of Radon transforms on complex projective spaces
• Range characterization of Radon transforms on \(S^ n\) and \(P^ n\mathbb{R}\)
• Range theorems and inversion formulas for Radon transforms on Grassmann manifolds
• Invariant differential operators on Grassmann manifolds
• The Radon transform on Euclidean spaces, compact two-point homogeneous spaces and Grassmann manifolds
• Complexes of straight lines in the space \(C^ n\)
• Spherical Functions on a Semisimple Lie Group, I
• Spherical Harmonics and Integral Geometry on Projective Spaces
• Some Problems in Integral Geometry and Some Related Problems in Micro-Local Analysis
• On the Range of the Radon d-Plane Transform and Its Dual
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