The behavior of Fourier transforms for nilpotent Lie groups

DOI10.1090/S0002-9947-96-01583-8zbMath0860.22005OpenAlexW1872845701WikidataQ115285224 ScholiaQ115285224MaRDI QIDQ4889950

Ronald L. Lipsman, Jonathan M. Rosenberg

Publication date: 21 April 1997

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

Full work available at URL: https://doi.org/10.1090/s0002-9947-96-01583-8

zbMATH Keywords

Fourier transformdistributionPaley-Wiener theoremnilpotent Lie groupvarietycomplexificationirreducible representationsorbit methodMoss's conjectureDixmier-Douady invariance

Mathematics Subject Classification ID

Radon transform (44A12) Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.) (22E27) (C^*)-algebras and (W^*)-algebras in relation to group representations (22D25) Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. (43A30)

Related Items (7)

Pompeiu sets in compact Heisenberg manifolds ⋮ A topological Paley-Wiener property for locally compact groups ⋮ Paley‐Wiener estimates for the Heisenberg group ⋮ Uncertainty principles on two step nilpotent Lie groups ⋮ Müntz-Szasz theorems for nilpotent Lie groups ⋮ Crossed products by \(C_0(X)\)-actions ⋮ Q.U.P. and Paley-Wiener properties of unimodular, especially nilpotent, Lie groups

Cites Work

• Unnamed Item
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• The structure of algebras of operator fields
• A description of the topology on the dual space of a nilpotent Lie group
• On the symplectic structure of coadjoint orbits of (solvable) Lie groups and applications. I
• The Radon transform
• Regularizations of twisted covariant systems and crossed products with continuous trace
• Orbits and primitive ideals of solvable Lie algebras
• A Paley-Wiener theorem for selected nilpotent Lie groups
• Some Remarks on the Pompeiu Problem for Groups
• Crossed Products of Continuous-Trace C ∗ -Algebras by Smooth Actions
• Paley-Wiener type theorem for the Heisenberg groups
• On Kirillov's character formula.
• Geometric Quantization and The Universal Enveloping Algebra of a Nilpotent Lie Group
• Dual topology of a nilpotent Lie group
• Square Integrable Representations of Nilpotent Groups
• An analogue of the Paley-Wiener theorem for the Heisenberg group

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