Seminário de Teoria de Operadores, Análise Complexa e Aplicações 

14/11/2013, 14:00 — 15:00 — Sala P3.10, Pavilhão de Matemática
Abdelhamid Boussejra, Université Ibn Tofail, Kenitra, Morocco.

The Hua operators on homogeneous line bundles over bounded symmetric domains of tube type

Let $𝒟=G/K$ be a bounded symmetric domain of tube type. We show that the image of the Poisson transform on the degenerate principal series representation of $G$ attached to the Shilov boundary of $𝒟$ is characterized by a $K$- covariant differential operator on a homogeneous line bundle over $𝒟$. As a consequence of our result we get the eigenvalues of the Casimir operator for Poisson transforms on homogeneous line bundles over $G/K$. This extends a result of Imemura and all on symmetric domains of classical type to all symmetric domains. Also we compute a class of Hua type integrals generalizing an earlier result of Faraut and Koranyi.