The Abel, Fourier and Radon transforms on symmetric spaces

DOI10.1016/S0019-3577(05)80039-4zbMath1112.44002arXivmath/0506049MaRDI QIDQ855600

Sigurdur Helgason

Publication date: 7 December 2006

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0506049

zbMATH Keywords

Fourier transformRadon transformsupport theoremAbel transform\(X\)-ray inversion\(X\)-ray transformhorocycle transformRiemann-Lebesgue's lemma

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Radon transform (44A12) Analysis on real and complex Lie groups (22E30) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Other transforms and operators of Fourier type (43A32)

Related Items

Spectral analysis on SL(2, \(\mathbb{R}\)) ⋮ A family of Hardy-type spaces on nondoubling manifolds ⋮ Radon transform on the torus ⋮ Abel transform on \(\mathrm{PSL}(2,\mathbb R)\) and some of its applications ⋮ Approximation by K-finite functions in \(L^p\) spaces ⋮ Paley‐Wiener estimates for the Heisenberg group ⋮ Beurling's theorem for Riemannian symmetric spaces II ⋮ Bernstein-Nikolskii and Plancherel-Polya inequalities in L_p-norms on non-compact symmetric spaces ⋮ X-ray transform on a symmetric space

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