On the Poisson transform on symmetric spaces of real rank one

DOI10.1006/jfan.2000.3590zbMath0963.43007OpenAlexW2019178900MaRDI QIDQ1577671

Alexandru D. Ionescu

Publication date: 22 June 2001

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jfan.2000.3590

zbMATH Keywords

Poisson transformsymmetric spaces of real rank one

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Analysis on real and complex Lie groups (22E30)

Related Items (14)

A characterization of the \(L^{2}\)-range of the Poisson transform related to Strichartz conjecture on symmetric spaces of noncompact type ⋮ Asymptotic mean value property for eigenfunctions of the Laplace-Beltrami operator on Damek-Ricci spaces ⋮ Spectral analysis on infinite Sierpiński fractafolds ⋮ A characterization of weak \(L^p\)-eigenfunctions of the Laplacian on homogeneous trees ⋮ An analogue of the spectral projection for homogeneous trees ⋮ Chaotic dynamics of the heat semigroup on the Damek-Ricci spaces ⋮ Image of the Schwartz space under spectral projection ⋮ A characterization of the \(L^2\)-range of the Poisson transforms on a class of vector bundles over the quaternionic hyperbolic spaces ⋮ The range of the spectral projection associated with the Dunkl Laplacian ⋮ Characterization of almost 𝐿^{𝑝}-eigenfunctions of the Laplace-Beltrami operator ⋮ Characterization of the Lp-range of the Poisson transform on the Octonionic Hyperbolic Plane ⋮ Fourier restriction theorem and characterization of weak \(L^2\) eigenfunctions of the Laplace-Beltrami operator ⋮ Unnamed Item ⋮ \(L^2\)-Poisson integral representations of eigensections of invariant differential operators on a homogeneous line bundle over the complex Grassmann manifold \(SU(r,r+b)/S( U(r)\times U(r+b))\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Some function spaces on symmetric spaces related to convolution operators
• Harmonic analysis as spectral theory of Laplacians
• Eigenspaces of the Laplacian ; integral representations and irreducibility
• Eigenfunctions of invariant differential operators on a symmetric space
• Expansions for spherical functions on noncompact symmetric spaces
• Corrigendum to ``Harmonic analysis as spectral theory of Laplacians
• Intertwining operators for semisimple groups
• Characterisations of Poisson integrals on symmetric spaces.

This page was built for publication: On the Poisson transform on symmetric spaces of real rank one