Spherical Harmonics and Integral Geometry on Projective Spaces

DOI10.2307/1999378zbMath0518.43006OpenAlexW4245490776MaRDI QIDQ3667384

Eric L. Grinberg

Publication date: 1983

Full work available at URL: https://doi.org/10.2307/1999378

zbMATH Keywords

Radon transformspheresspherical harmonicsrepresentationsLaplace-Beltrami operatorprojective spacesintegral geometryHopf fibrationcompact 2-point homogeneous spaces

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Integral geometry (53C65) Harmonic analysis and spherical functions (43A90)

Related Items

Range characterization of Radon transforms on quaternionic projective spaces, On images of Radon transforms, Asymptotic representation theory and the spectrum of a random geometric graph on a compact Lie group, Support theorems for real-analytic Radon transforms, Harmonic Analysis on Grassmannian Bundles, Quantization of the Laplacian operator on vector bundles. I, Bootstrap bounds on closed Einstein manifolds, Balanced metrics and Chow stability of projective bundles over Kähler manifolds II, Integral geometry on Grassmann manifolds and calculus of invariant differential operators, Riesz and Green energy on projective spaces, Intersection Bodies and the Busemann-Petty Problem, Isometric embeddings of finite-dimensional $\ell_p$-spaces over the quaternions, Approximation of smooth functions on compact two-point homogeneous spaces, On Radon transforms on compact Lie groups, Distributions of truncations of the heat kernel on the complex projective space, Densities of generalized stochastic areas and windings arising from Anti-de Sitter and Hopf fibrations, Spherical Radon transform and related wavelet transforms, Inversion formulas for the \(k\)-dimensional Radon transform in real hyperbolic spaces, Inversion and characterization of the hemispherical transform, Evaluating the Mahler measure of linear forms via the Kronecker limit formula on complex projective space

Cites Work

• The Radon transform
• \(L^ p\) estimates for Radon transforms in Euclidean and non-Euclidean spaces
• The Radon transform on Zoll surfaces
• The Radon transform on Euclidean spaces, compact two-point homogeneous spaces and Grassmann manifolds
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item