標題: | The direct integral of some weighted Bergman spaces |
作者: | Chuah, Meng-Kiat 應用數學系 Department of Applied Mathematics |
關鍵字: | Bergman space;direct integral;unitary representation;model |
公開日期: | 1-Feb-2007 |
摘要: | Let G be the abelian Lie group R(n) x R(k)/Z(k), acting on the complex space X = R(n+k) x iG. Let F be a strictly convex function on R(n+k). Let H be the Bergman space of holomorphic functions on X which are square-integrable with respect to the weight e(-F). The G-action on X leads to a unitary G-representation on the Hilbert space H. We study the irreducible representations which occur in H by means of their direct integral. This problem is motivated by geometric quantization, which associates unitary representations with invariant Kahler forms. As an application, we construct a model in the sense that every irreducible G-representation occurs exactly once in H. |
URI: | http://dx.doi.org/10.1017/S0013091505000453 http://hdl.handle.net/11536/11159 |
ISSN: | 0013-0915 |
DOI: | 10.1017/S0013091505000453 |
期刊: | PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY |
Volume: | 50 |
Issue: | |
起始頁: | 115 |
結束頁: | 122 |
Appears in Collections: | Articles |