On the Boundary Behaviour of Generalized Poisson Integrals on Symmetric Spaces

DOI10.2307/1999794zbMath0582.43008OpenAlexW4237641997MaRDI QIDQ3705930

Henrik Schlichtkrull

Publication date: 1985

Full work available at URL: https://doi.org/10.2307/1999794

zbMATH Keywords

uniform convergenceFatou theoremboundary valuesIwasawa decompositionPoisson transformsimple rootsPoisson integralsRiemannian symmetric spaceSatake-Furstenberg compactification

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Differential geometry of symmetric spaces (53C35) Boundary value problems on manifolds (58J32)

Related Items (4)

Dixmier trace for Toeplitz operators on symmetric domains ⋮ Fractional Laplacians and extension problems: The higher rank case ⋮ Fatou theorem and its converse for positive eigenfunctions of the Laplace-Beltrami operator on harmonic \textit{NA} groups ⋮ Ergodic boundary representations

Cites Work

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• Hyperfunctions and harmonic analysis on symmetric spaces
• A Fatou theorem for eigenfunctions of the Laplace-Beltrami operator in a symmetric space
• Boundary behavior of harmonic functions on symmetric spaces: maximal estimates for Poisson integrals
• Topics in harmonic analysis on homogeneous spaces
• Representations of real reductive Lie groups
• Poisson integrals and boundary components of symmetric spaces
• A realization of Riemannian symmetric spaces
• Eigenfunctions of invariant differential operators on a symmetric space
• Fatou's theorem for symmetric spaces. I
• A duality for symmetric spaces with applications to group representations
• Fatou's theorem for symmetric spaces
• Poisson integrals and semisimple groups
• A Fatou-type theorem for harmonic functions on symmetric spaces
• Fatou Theorems for Eigenfunctions of the Invariant Differential Operators on Symmetric Spaces

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