Triplets of Closely Embedded Dirichlet Type Spaces on the Unit Polydisc |
| |
Authors: | Petru Cojuhari Aurelian Gheondea |
| |
Institution: | 1. Department of Applied Mathematics, AGH University of Science and Technology, Al.?Mickievicza 30, 30-059, Cracow, Poland 2. Department of Mathematics, Bilkent University, 06800, Bilkent, Ankara, Turkey 3. Institutul de Matematic? al Academiei Romane, C.P. 1-764, 014700, Bucure?ti, Romania
|
| |
Abstract: | We propose a general concept of triplet of Hilbert spaces with closed embeddings, instead of continuous ones, and we show how rather general weighted $L^2$ spaces yield this kind of generalized triplets of Hilbert spaces for which the underlying spaces and operators can be explicitly calculated. Then we show that generalized triplets of Hilbert spaces with closed embeddings can be naturally associated to any pair of Dirichlet type spaces $\mathcal{D }_\alpha (\mathbb{D }^N)$ of holomorphic functions on the unit polydisc $\mathbb{D }^N$ and we explicitly calculate the associated operators in terms of reproducing kernels and radial derivative operators. We also point out a rigging of the Hardy space $H^2(\mathbb{D }^N)$ through a scale of Dirichlet type spaces and Bergman type spaces. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|