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

Universite Henri Poincare

Genkai Zhang

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Journal of Functional Analysis

0022-1236 (ISSN) 1096-0783 (eISSN)

Vol. 262 9 4140-4159

Subject Categories

Mathematics

DOI

10.1016/j.jfa.2012.02.012

More information

Created

10/7/2017