Q.U.P. and Paley-Wiener properties of unimodular, especially nilpotent, Lie groups

DOI10.1090/S0002-9939-97-03608-3zbMath0866.43002WikidataQ115289223 ScholiaQ115289223MaRDI QIDQ3127290

Didier Arnal, Jean Ludwig

Publication date: 8 April 1997

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

zbMATH Keywords

Paley-Wiener theoremuncertainty principlelocally compact unimodular group

Mathematics Subject Classification ID

Nilpotent and solvable Lie groups (22E25) Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. (43A30)

Related Items (14)

Boundedness and uniqueness of quaternion Weyl transform ⋮ Admissible vectors for the regular representation ⋮ The Levi problem on strongly pseudoconvex \(G\)-bundles ⋮ Paley-Wiener theorems for the \(\mathrm U(n)\)-spherical transform on the Heisenberg group ⋮ Invertibility of positive Toeplitz operators and associated uncertainty principle ⋮ Benedicks–Amrein–Berthier theorem for the Heisenberg motion group ⋮ Generalized Fredholm properties for invariant pseudodifferential operators ⋮ Bergman spaces of natural \(G\)-manifolds ⋮ Unitary representations of unimodular Lie groups in Bergman spaces ⋮ Restrictions of irreducible unitary representations of nilpotent Lie groups to lattices ⋮ A COMPACT QUALITATIVE UNCERTAINTY PRINCIPLE FOR SOME NONUNIMODULAR GROUPS ⋮ Benedicks’ theorem for the Heisenberg group ⋮ A topological Paley-Wiener property for locally compact groups ⋮ Qualitative uncertainty principles for groups with finite dimensional irreducible representations

Cites Work

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• Opérateurs de rang fini dans les représentations unitaires
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• *-products in the method of orbits for nilpotent groups
• On support properties of Lsup(p)-functions and their Fourier transforms
• Good ideals in the group algebra of a nilpotent Lie group
• On the nilpotent \(*\)-Fourier transform
• A Paley-Wiener theorem for selected nilpotent Lie groups
• A Qualitative Uncertainty Principle for Unimodular Groups of Type I
• The behavior of Fourier transforms for nilpotent Lie groups
• A Qualitative Uncertainty Principle for Certain Locally Compact Groups

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