Please use this identifier to cite or link to this item:
doi:10.22028/D291-26332
Title: | Beurling-type representation of invariant subspaces in reproducing kernel Hilbert spaces |
Author(s): | Barbian, Christoph |
Language: | English |
Year of Publication: | 2006 |
DDC notations: | 510 Mathematics |
Publikation type: | Other |
Abstract: | By Beurling´s theorem, the orthogonal projection onto an invariant subspace M of the Hardy space H^{2}(\mathbb{D}) on the complex unit disk can be represented as P_{M}=M_{\phi}M_{\phi}^{*} where \phi is a suitable multiplier of H^{2}(\mathbb{D}). This concept can be carried over to arbitrary Nevanlinna-Pick spaces but fails in more general settings. This paper introduces the notion of Beurling decomposability of subspaces. An invariant subspace M of a reproducing kernel space will be called Beurling decomposable if there exist (operator-valued) multipliers \phi_{1},\phi_{2} such that P_{M}=M_{\phi_{1}}M_{\phi_{1}}^{*}-M_{\phi_{2}}M_{\phi_{2}}^{*} and M=\textrm{ran}M_{\phi_{1}}. We characterize the finite-codimensional and the finite-rank Beurling-decomposable subspaces by means of the core function and the core operator. As an application, we show that in many analytic Hilbert modules \mathcal{H}, every fnite-codimensional submodule M can be written as M=\sum_{i=1}^{r}p_{i}\mathcal{H} with suitable polynomials p_{i}. |
Link to this record: | urn:nbn:de:bsz:291-scidok-46359 hdl:20.500.11880/26388 http://dx.doi.org/10.22028/D291-26332 |
Series name: | Preprint / Fachrichtung Mathematik, Universität des Saarlandes |
Series volume: | 167 |
Date of registration: | 9-Mar-2012 |
Faculty: | MI - Fakultät für Mathematik und Informatik |
Department: | MI - Mathematik |
Collections: | SciDok - Der Wissenschaftsserver der Universität des Saarlandes |
Files for this record:
File | Description | Size | Format | |
---|---|---|---|---|
preprint_167_06.pdf | 221,04 kB | Adobe PDF | View/Open |
Items in SciDok are protected by copyright, with all rights reserved, unless otherwise indicated.