"Two Characterizations of Dirichlet Spaces"
HAKKI TURGAY KAPTANOĞLU
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
Place: Mathematics Seminar Room, SA-141
Tea and cookies will be served before the seminar.