𝐿^{𝑝} version of Hardy’s theorem on semisimple Lie groups

DOI10.1090/S0002-9939-02-06272-XzbMath0996.43005OpenAlexW1510546093WikidataQ115290184 ScholiaQ115290184MaRDI QIDQ2781358

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Publication date: 19 March 2002

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-02-06272-x

zbMATH Keywords

uncertainty principlesemisimple Lie groupsHardy's theorem

Mathematics Subject Classification ID

Analysis on real and complex Lie groups (22E30) Semisimple Lie groups and their representations (22E46) Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. (43A30)

Related Items (16)

Hardy's uncertainty principle on hyperbolic spaces ⋮ Cowling-Price theorem and characterization of heat kernel on symmetric spaces ⋮ On theorems of Hardy, Gelfand-Shilov and Beurling for semisimple groups ⋮ On the theorems of Hardy and Miyachi for the Jacobi–Dunkl transform ⋮ The Abel, Fourier and Radon transforms on symmetric spaces ⋮ AN ANALOGUE OF COWLING–PRICE'S THEOREM AND HARDY'S THEOREM FOR THE GENERALIZED FOURIER TRANSFORM ASSOCIATED WITH THE SPHERICAL MEAN OPERATOR ⋮ Beurling's theorem for \(\mathrm{SL} (2, {\mathbb{R}})\) ⋮ Hardy's theorem for the continuous wavelet transform ⋮ Uncertainty principle and \(L^{p}\)--\(L^{q}\)-sufficient pairs on noncompact real symmetric spaces ⋮ An \(L^{p}\)-\(L^{q}\)-version of Morgan's theorem for the \(n\)-dimensional Euclidean motion group ⋮ Uncertainty principle andL^p–L^q-version of morgan’s theorem on semi-simple lie groups ⋮ The uncertainty principle on Riemannian symmetric spaces of the noncompact type ⋮ Uncertainty principles on two step nilpotent Lie groups ⋮ Beurling's theorem for Riemannian symmetric spaces II ⋮ Uncertainty principle and (L^p,L^q)sufficient pairs on Chébli–Trimèche hypergroups ⋮ The Lp –Lq version of Hardy's Theorem on nilpotent Lie groups

Cites Work

• The heat kernel and Hardy's theorem on symmetric spaces of noncompact type
• The spherical Fourier transform of rapidly decreasing functions. A simple proof of a characterization due to Harish-Chandra, Helgason, Trombi, and Varadarajan
• A uniqueness theorem of Beurling for Fourier transform pairs
• The uncertainty principle: A mathematical survey
• An analogue of Hardy's theorem for very rapidly decreasing functions on semi-simple Lie groups
• Hardy's uncertainty principle on semisimple groups
• A generalization of the Hardy theorem to semisimple Lie groups
• Hardy's Uncertainty Principle on Certain Lie Groups
• A Theorem Concerning Fourier Transforms
• An analogue of Hardy’s theorem for semi-simple Lie groups
• Uncertainty principles on two step nilpotent Lie groups
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