**"****Two Characterizations of Dirichlet Spaces****"**

By

**HAKKI TURGAY KAPTANOĞLU**

**(BİLKENT UNIVERSITY)**

**Abstract: ** Dirichlet spaces D_q
indexed with real q are those Hilbert spaces of holomorphic
functions on the unit ball B of C^N with binomial reproducing kernels for
q>-(1+N) and hypergeometric reproducıng
kernels otherwise. They include the Bergman, Hardy, Arveson,
and classical Dirichlet spaces as special cases. We
first obtain a characterization of Dirichlet spaces
using a double integral on B*B of a difference quotient extending the work of Rochberg and Wu. We then show the uniqueness of the Dirichlet spaces with integer q on the unit disc among Möbius-type invariant Hilbert spaces extending the work of Arazy and Fisher.

**Date: ****Tuesday, November 11, 2014**

**Time: ****15:40**

**Place: ****Mathematics Seminar Room,
SA-141**

Tea and cookies will be served before the
seminar.