\(L^2\)-Poisson integral representations of eigensections of invariant differential operators on a homogeneous line bundle over the complex Grassmann manifold \(SU(r,r+b)/S( U(r)\times U(r+b))\)

DOI10.1007/s10455-021-09819-9zbMath1497.43009OpenAlexW4206404017WikidataQ115384524 ScholiaQ115384524MaRDI QIDQ2116414

Noureddine Imesmad, Abdelhamid Boussejra, Achraf Ouald Chaib

Publication date: 17 March 2022

Published in: Annals of Global Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10455-021-09819-9

zbMATH Keywords

Poisson transformFourier restriction estimateStrichartz conjectureasymptotic expansion for the Poisson transform

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Harmonic analysis on homogeneous spaces (43A85) Differential geometry of symmetric spaces (53C35)

Related Items

A characterization of the \(L^2\)-range of the Poisson transforms on a class of vector bundles over the quaternionic hyperbolic spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A characterization of the \(L^{2}\)-range of the Poisson transform related to Strichartz conjecture on symmetric spaces of noncompact type
• Harmonic analysis as spectral theory of Laplacians
• A formula for the hypergeometric function of type \(BC_n\)
• A new proof of a Paley-Wiener type theorem for the Jacobi transform
• \(L^2\)-concrete spectral analysis of the invariant Laplacian \(\Delta_{\alpha\beta}\) in the unit complex ball \(B^n\)
• The Plancherel formula for spherical functions with a one-dimensional \(K\)-type on a simply connected simple Lie group of Hermitian type
• On the Poisson transform on symmetric spaces of real rank one
• The Helgason Fourier transform for homogeneous vector bundles over Riemannian symmetric spaces
• Fourier restriction theorem and characterization of weak \(L^2\) eigenfunctions of the Laplace-Beltrami operator
• A duality for symmetric spaces with applications to group representations
• Spherical Functions on a Semisimple Lie Group, I
• A Basic Inequality for Scattering Theory on Riemannian Symmetric Spaces of the Noncompact Type
• Characterization of the Lp-range of the Poisson transform on the Octonionic Hyperbolic Plane
• Characterization of almost 𝐿^{𝑝}-eigenfunctions of the Laplace-Beltrami operator

This page was built for publication: \(L^2\)-Poisson integral representations of eigensections of invariant differential operators on a homogeneous line bundle over the complex Grassmann manifold \(SU(r,r+b)/S( U(r)\times U(r+b))\)