On the Poisson transform on a homogenous vector bundle over the quaternionic hyperbolic space

DOI10.5802/CRMATH.550MaRDI QIDQ6496635

Achraf Ouald Chaib

Publication date: 6 May 2024

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Analysis on real and complex Lie groups (22E30) Differential geometry of symmetric spaces (53C35)

Cites Work

• A characterization of the \(L^{2}\)-range of the Poisson transform related to Strichartz conjecture on symmetric spaces of noncompact type
• Eigenfunctions of invariant differential operators on a symmetric space
• Vector valued Poisson transforms on Riemannian symmetric spaces of rank one
• On the Poisson transform on symmetric spaces of real rank one
• \(L^2\)-Poisson integral representations of eigensections of invariant differential operators on a homogeneous line bundle over the complex Grassmann manifold \(SU(r,r+b)/S( U(r)\times U(r+b))\)
• Poisson transforms on vector bundles
• Hardy-type spaces for eigenfunctions of invariant differential operators on homogeneous line bundles over Hermitian symmetric spaces
• Characterization of almost 𝐿^{𝑝}-eigenfunctions of the Laplace-Beltrami operator
• On Poisson transforms for spinors
• A characterization of the \(L^2\)-range of the Poisson transforms on a class of vector bundles over the quaternionic hyperbolic spaces
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