Hua operators, Poisson transform and relative discrete series on line bundles over bounded symmetric domains
Journal article, 2012
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.
Eigenfunctions
Shilov boundary
Poisson transform
Hua operators
Spaces
Tube type
Operators
Invariant differential-operators
Bounded symmetric domains
Invariant differential
Kernels
Representations
Author
K. Koufany
Henri Poincaré University
Genkai Zhang
Chalmers, Mathematical Sciences, Mathematics
University of Gothenburg
Journal of Functional Analysis
0022-1236 (ISSN) 1096-0783 (eISSN)
Vol. 262 9 4140-4159Subject Categories
Mathematics
DOI
10.1016/j.jfa.2012.02.012