Generalized notions of harmonic functions symmetric spaces

DOI10.1007/BF02924810zbMath0519.22008OpenAlexW2062718214MaRDI QIDQ3669661

Adam Korányi

Publication date: 1981

Published in: Rendiconti del Seminario Matematico e Fisico di Milano (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02924810

zbMATH Keywords

harmonic functionPoisson integralBergman metricShilov boundaryinvariant differential operatornon-compact symmetric spaceparabolic groupCartan domain of tube type

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Analysis on real and complex Lie groups (22E30) Semisimple Lie groups and their representations (22E46) Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) (32M15)

Cites Work

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• The Hua operators on bounded symmetric domains of tube type
• Poisson formula and compound diffusion associated to an overdetermined elliptic system on the Siegel halfplane of rank two
• Poisson integrals and boundary components of symmetric spaces
• Eigenfunctions of invariant differential operators on a symmetric space
• Differential equations and the Bergman-Silov boundary on the Siegel upper half plane
• Realization of Hermitian symmetric spaces as generalized half-planes
• The Poisson integral for generalized half-planes and bounded symmetric domains
• A Poisson formula for semi-simple Lie groups
• Group invariance of Cauchy's formula in several variables
• Remarks on a theorem of Koranyi and Malliavin on the Siegel upper half plane of rank two
• A Fatou-type theorem for harmonic functions on symmetric spaces
• Compactifications of Symmetric Spaces

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