The Helgason Fourier transform for homogeneous vector bundles over Riemannian symmetric spaces

DOI10.2140/PJM.1997.179.263zbMath0871.43006OpenAlexW1992088190WikidataQ115230691 ScholiaQ115230691MaRDI QIDQ1816503

Roberto Camporesi

Publication date: 9 September 1997

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2140/pjm.1997.179.263

zbMATH Keywords

spherical functionssemisimple Lie groupsHelgason Fourier transformhomogeneous vector bundlesnoncompact Riemannian symmetric space

Mathematics Subject Classification ID

Semisimple Lie groups and their representations (22E46) Differential geometry of symmetric spaces (53C35) Harmonic analysis and spherical functions (43A90)

Related Items (6)

Resonances of the Laplace operator on homogeneous vector bundles on symmetric spaces of real rank-one ⋮ On the analogy between real reductive groups and Cartan motion groups: contraction of irreducible tempered representations ⋮ A characterization of the \(L^2\)-range of the Poisson transforms on a class of vector bundles over the quaternionic hyperbolic spaces ⋮ Harmonic analysis for differential forms on complex hyperbolic spaces ⋮ The Helgason Fourier transform for homogeneous vector bundles over compact Riemannian symmetric spaces -- the local theory ⋮ \(L^2\)-Poisson integral representations of eigensections of invariant differential operators on a homogeneous line bundle over the complex Grassmann manifold \(SU(r,r+b)/S( U(r)\times U(r+b))\)

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