On the nilpotent \(*\)-Fourier transform

DOI10.1007/BF00761419zbMath0798.22004MaRDI QIDQ1314804

Hamid Zahir, Jean Ludwig

Publication date: 3 November 1994

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Fourier transformdistributionsLie algebraconvolution productSchwartz spacesimply connected nilpotent Lie groupdiffeomorphic parametrizationMoyal \(*\)-product

Mathematics Subject Classification ID

Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.) (22E27) Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. (43A30)

Related Items (8)

Compact actions, retract theory and prime ideals ⋮ A smooth family of intertwining operators ⋮ Sub-Laplacians of holomorphic \(L^p\)-type on rank one AN-groups and related solvable groups ⋮ Nilpotent Lie groups: Fourier inversion and prime ideals ⋮ Entrelacement des restrictions des représentations unitaires des groupes de Lie nilpotents. (Intertwining of restriction of unitary representations of nilpotent Lie groups) ⋮ The Paley-Wiener theorem for certain nilpotent Lie groupsJean ⋮ Q.U.P. and Paley-Wiener properties of unimodular, especially nilpotent, Lie groups ⋮ The \(C^\ast\)-algebras of connected real two-step nilpotent Lie groups

Cites Work

• Unnamed Item
• Adapted Fourier transform of Schwartz spaces for certain nilpotent Lie groups
• *-products in the method of orbits for nilpotent groups
• La structure de Poisson sur l'algèbre symétrique d'une algèbre de Lie nilpotente

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