The Helgason Fourier transform for compact Riemannian symmetric spaces of rank one

DOI10.1007/BF02392752zbMath0707.43001OpenAlexW2058568741WikidataQ115392309 ScholiaQ115392309MaRDI QIDQ919562

Thomas O. Sherman

Publication date: 1990

Published in: Acta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02392752

zbMATH Keywords

inversion formulasgeometrical Helgason Fourier transformglobal Fourier transform kernelPlancherel theoremsRiemannian symmetric spaces of the compact type

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Global Riemannian geometry, including pinching (53C20) Differential geometry of symmetric spaces (53C35) Harmonic analysis and spherical functions (43A90) Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups (43A25)

Related Items (11)

Genuinely sharp heat kernel estimates on compact rank-one symmetric spaces, for Jacobi expansions, on a ball and on a simplex ⋮ Orthogonal polynomials and diffusion operators ⋮ Ramanujan's master theorem and duality of symmetric spaces ⋮ Riesz transforms on compact Riemannian symmetric spaces of rank one ⋮ Symmetric Diffusions with Polynomial Eigenvectors ⋮ Hörmander class of pseudo-differential operators on compact Lie groups and global hypoellipticity ⋮ A Hardy inequality for ultraspherical expansions with an application to the sphere ⋮ The Helgason Fourier transform for homogeneous vector bundles over compact Riemannian symmetric spaces -- the local theory ⋮ Fourier series on compact symmetric spaces: \(K\)-finite functions of small support ⋮ Theorems of Chernoff and Ingham for certain eigenfunction expansions ⋮ On a theorem of Chernoff on rank one Riemannian symmetric spaces

Cites Work

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• A duality for symmetric spaces with applications to group representations
• Hilbert and Fourier Transforms on a Sphere
• Fourier Analysis on the Sphere
• Fourier analysis on compact symmetric space
• Elementary spherical functions on symmetric spaces.
• Radon-Fourier transforms on symmetric spaces and related group representations

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