\(L^{2}\)-Poisson integral representations of solutions of the Hua system on the bounded symmetric domain \(SU(n,n)\)/\(S(U(n){\times}U(n))\)

DOI10.1016/S0022-1236(03)00062-4zbMath1029.22014MaRDI QIDQ1403837

Abdelhamid Boussejra

Publication date: 4 September 2003

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

zbMATH Keywords

Poisson integraldifferential operatorbounded symmetric domainShilov boundaryHua operator

Mathematics Subject Classification ID

Integral representations of solutions to PDEs (35C15) Analysis on real and complex Lie groups (22E30)

Related Items (8)

L^p-Poisson integral representations of solutions of the Hua system on the Lie ball in ℂⁿ ⋮ Lifted infinitesimal holomorphic representation for the \(n\)-dimensional complex hyperbolic ball and for Cartan domains of type I ⋮ \(L^p\)-Poisson integral representations for solutions of the generalized Hua system on line bundles over \(SU (n, n) / S(U(n) \times U(n))\) ⋮ \(L^p\)-Poisson integral representations of solutions of the Hua system on Hermitian symmetric spaces of tube type ⋮ An explicit expression for the Harish-Chandra c-function for the homogeneous space \(SO(2,n)/S(O(2)\times O(n)), \, n\in \{ 2,4,6\}\) ⋮ Fatou's theorems and a generalized Poisson transform of anL^p-function over the Shilov boundary of the bounded symmetric domain of type I ⋮ L²-Poisson integral representations of solutions of the Hua system on the ball in ℂ² ⋮ The generalized spherical function for odd-dimensional bounded symmetric domains of type IV

Cites Work

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• Les équations de Hua d'un domaine borné symétrique du type tube. (The equations of Hua for a bounded symmetric domain of tube type)
• 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
• Hua operators on bounded homogeneous domains in \(\mathbb{C}^ n\) and alternative reproducing kernels for holomorphic functions
• Boundary value problems for the Shilov boundary of a bounded symmetric domain of tube type
• The Poisson integral for generalized half-planes and bounded symmetric domains
• Function spaces and reproducing kernels on bounded symmetric domains
• Solutions du système d'équations différentielles de Hua et intégrales de Poisson-Shilov des fonctions de carré intégrable sur la frontière de Shilov de la boule matricielle de rang deux

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