A weighted Plancherel formula. III: The case of the hyperbolic matrix ball

zbMath0836.43018MaRDI QIDQ1318629

Jaak Peetre, Genkai Zhang

Publication date: 6 April 1994

Published in: Collectanea Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/39596

zbMATH Keywords

Weyl grouporbitsspherical functionshypergeometric functionstensor productsLaplace operatorreproducing kernelsholomorphic discrete series representationsweighted Bergman spaceweighted measureSU(2,2)Harish-Chandra \(\mathbf c\)- functionhyperbolic matrix ballK-invariant eigenfunctions

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Semisimple Lie groups and their representations (22E46) Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) (32M15) Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis) (43A65) Harmonic analysis and spherical functions (43A90)

Related Items (7)

Unnamed Item ⋮ Hermitian symmetric spaces of tube type and multivariate Meixner-Pollaczek polynomials ⋮ The \(C\)-version Segal-Bargmann transform for finite Coxeter groups defined by the restriction principle ⋮ Berezin transforms on the \(2\times 2\) matrix space related to the \(U(2)\times U(2)\)-action ⋮ Relative discrete series of line bundles over bounded symmetric domains ⋮ Unnamed Item ⋮ Branching coefficients of holomorphic representations and Segal-Bargmann transform

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