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Hua operators, Poisson transform and relative discrete series on line bundles over bounded symmetric domains

K. Koufany ; Genkai Zhang (Institutionen för matematiska vetenskaper, matematik)
Journal of Functional Analysis (0022-1236). Vol. 262 (2012), 9, p. 4140-4159.
[Artikel, refereegranskad vetenskaplig]

For bounded symmetric domains Omega = G/K of tube type and general domains of type 1, we consider the action of G on sections of a homogeneous line bundle over Omega and the corresponding eigenspaces of G-invariant differential operators. The Poisson transform maps hyperfunctions on the Shilov boundary S=K/L to the eigenspaces. We characterize the image in terms of twisted Hua operators. For some special parameters the Poisson transform is of Szego type whose image is in a relative discrete series; we compute the corresponding elements in the discrete series.

Nyckelord: Bounded symmetric domains, Shilov boundary, Invariant differential, Operators, Eigenfunctions, Poisson transform, Hua operators, Invariant differential-operators, Tube type, Representations, Kernels, Spaces

Denna post skapades 2012-04-19. Senast ändrad 2015-12-17.
CPL Pubid: 156872


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