Harmonic Analysis on Grassmannian Bundles

DOI10.2307/2000581zbMath0618.43005OpenAlexW4244881659MaRDI QIDQ4727646

Robert S. Strichartz

Publication date: 1986

Full work available at URL: https://doi.org/10.2307/2000581

zbMATH Keywords

Radon transformPlancherel formulasemidirect productGrassmannian bundles

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Harmonic analysis on homogeneous spaces (43A85) Analysis on real and complex Lie groups (22E30)

Related Items (20)

Moment conditions and support theorems for Radon transforms on affine Grassmann manifolds ⋮ Radon transform on real, complex, and quaternionic Grassmannians ⋮ On images of Radon transforms ⋮ Radon transforms on affine Grassmannians ⋮ Dual Radon transforms on affine Grassmann manifolds ⋮ Orbital Parameters for Induced and Restricted Representations ⋮ Funk, cosine, and sine transforms on Stiefel and Grassmann manifolds ⋮ Radon transforms on Grassmann manifolds ⋮ Norm estimates for \(k\)-plane transforms and geometric inequalities ⋮ On Radon transforms between lines and hyperplanes ⋮ Higher-rank Radon transforms on constant curvature spaces ⋮ New inversion formulas for Radon transforms on affine Grassmannians ⋮ Bi-invariant differential operators on the Euclidean motion group and applications to generalized Radon transforms ⋮ End point estimates for Radon transform of radial functions on non-Euclidean spaces ⋮ The \(\lambda \)-cosine transforms, differential operators, and Funk transforms on Stiefel and Grassmann manifolds ⋮ Riesz potentials and orthogonal Radon transforms on affine Grassmannians ⋮ Invariant differential operators on Grassmann manifolds ⋮ Book Review: Integral geometry and Radon transforms ⋮ Convolution algebras for Heckman-Opdam polynomials derived from compact Grassmannians ⋮ Strichartz's Radon transforms for mutually orthogonal affine planes and fractional integrals

Cites Work

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• \(L^ p\) estimates for Radon transforms in Euclidean and non-Euclidean spaces
• Invariant differential operators on Grassmann manifolds
• A duality for symmetric spaces with applications to group representations
• Les espaces symétriques noncompacts
• Spherical Harmonics and Integral Geometry on Projective Spaces
• Bochner Identities for Fourier Transforms
• Some results on eigenfunctions on symmetric spaces and eigenspace representations.
• The Hardy Space H¹ on Manifolds and Submanifolds

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