On theorems of Beurling and Hardy for the Euclidean motion groups

DOI10.2748/tmj/1128703001zbMath1085.22004OpenAlexW2034891113MaRDI QIDQ812888

Rudra P. Sarkar, Sundaram Thangavelu

Publication date: 26 January 2006

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.tmj/1128703001

zbMATH Keywords

Hardy's theoremBeurling's theoremMotion group

Mathematics Subject Classification ID

Analysis on real and complex Lie groups (22E30) Analysis on other specific Lie groups (43A80)

Related Items (15)

Generalized analogs of the Heisenberg uncertainty inequality ⋮ Variants of Müntz-Szàsz analogs for Euclidean spin groups ⋮ On Hardy's uncertainty principle for solvable locally compact groups ⋮ An Analogue of Beurling's Theorem for the Heisenberg Group ⋮ Hardy's theorem for Gabor transform on nilpotent Lie groups ⋮ Analogues of Miyachi, Cowling-Price and Morgan theorems for compact extensions of \(\mathbb R^{n1}\) ⋮ Uncertainty principles for Heisenberg motion group ⋮ A generalized Beurling theorem for some Lie groups ⋮ An \(L^{p}\)-\(L^{q}\)-version of Morgan's theorem for the \(n\)-dimensional Euclidean motion group ⋮ On theorems of Beurling and Cowling-Price for certain nilpotent Lie groups ⋮ Unnamed Item ⋮ A generalizaton of Hardy's uncertainty principle on compact extensions of \(\mathbb R^n\) ⋮ Beurling's theorem for nilpotent Lie groups ⋮ HARDY AND MIYACHI THEOREMS FOR HEISENBERG MOTION GROUPS ⋮ HARDY’S THEOREM FOR GABOR TRANSFORM

Cites Work

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• A uniqueness theorem of Beurling for Fourier transform pairs
• An analogue of the Hardy theorem for the Cartan motion group
• An analogue of Hardy's theorem for very rapidly decreasing functions on semi-simple Lie groups
• Hermite functions and uncertainty principles for the Fourier and the windowed Fourier trans\-forms.
• Revisiting Hardy's theorem for the Heisenberg group
• Hardy's uncertainty principle on semisimple groups
• Harmonic analysis on the group of rigid motions of the Euclidean plane
• Hardy’s theorem for the 𝑛-dimensional Euclidean motion group
• A complete analogue of Hardy's theorem on semisimple Lie groups
• Hardy's theorem for the helgason Fourier transform on noncompact rank one symmetric spaces

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