Eigenvalues of generalized Laplacians for generalized Poisson-Cauchy transforms on classical domains

DOI10.32917/HMJ/1249046339zbMath1179.43008OpenAlexW1515665034WikidataQ128870734 ScholiaQ128870734MaRDI QIDQ730696

Michiroh Tsukamoto, Eisuke Imamura, Kiyosato Okamoto

Publication date: 12 October 2009

Published in: Hiroshima Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.32917/hmj/1249046339

zbMATH Keywords

Casimir operatorLaplace-Beltrami operatorsLie group representationseigenvalues of generalized LaplaciansHarish-Chandra decompositionharmonic analysis on symmetric spaceshomogeneous holomorphic line bundles over hermitian symmetric spacesHua's differential operatorPoisson-Cauchy transforms on classical domains

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) Integral representations, constructed kernels (e.g., Cauchy, Fantappiè-type kernels) (32A26) Proceedings, conferences, collections, etc. pertaining to abstract harmonic analysis (43-06)

Related Items (3)

\(L^p\)-Poisson integral representations for solutions of the generalized Hua system on line bundles over \(SU (n, n) / S(U(n) \times U(n))\) ⋮ Generalized Laplacians for generalized Poisson-Cauchy transforms on classical domains ⋮ Poisson Transforms for Line Bundles from the Shilov Boundary to Bounded Symmetric Domains

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