Hua operators, Poisson transform and relative discrete series on line bundles over bounded symmetric domainsReport as inadecuate




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1 Analyse IECL - Institut Élie Cartan de Lorraine 2 Chalmers University of Technology Gothenburg

Abstract : Let Ω = G-K be a bounded symmetric domain and S = K-L its Shilov boundary. We consider the action of G on sections of a homogeneous line bundle over Ω and the corresponding eigenspaces of G-invariant differential operators. The Poisson transform maps hyperfunctions on S to the eigenspaces. We characterize the image in terms of twisted Hua operators. For some special parameters the Poisson transform is of Szegö type whose image is in a relative discrete series; we compute the corresponding elements in the discrete series.





Author: Khalid Koufany - Genkai Zhang -

Source: https://hal.archives-ouvertes.fr/



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