Contents/conteúdo

Mathematics Department Técnico Técnico

Operator Theory, Complex Analysis and Applications Seminar  RSS

Sessions

14/11/2013, 14:00 — 15:00 — Room P3.10, Mathematics Building
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.


Seminar organized in the context of the project PTDC/MAT/121837/2010.

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