On the Brown--Shields conjecture for cyclicity in the Dirichlet space
| dc.creator | El-Fallah, Omar | |
| dc.creator | Kellay, Karim | |
| dc.creator | Ransford, Thomas | |
| dc.date | 2008-09-26 | |
| dc.date.accessioned | 2026-07-07T10:05:41Z | |
| dc.date.available | 2026-07-07T10:05:41Z | |
| dc.description | Let $\cD$ be the Dirichlet space, namely the space of holomorphic functions on the unit disk whose derivative is square-integrable. We establish a new sufficient condition for a function $f\in\cD$ to be {\em cyclic}, i.e. for $\{pf: p\text{a polynomial}\}$ to be dense in $\cD$. This allows us to prove a special case of the conjecture of Brown and Shields that a function is cyclic in $\cD$ iff it is outer and its zero set (defined appropriately) is of capacity zero. | |
| dc.identifier | https://arxiv.org/abs/0809.4557 | |
| dc.identifier | http://arxiv.org/abs/0809.4557 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/170079 | |
| dc.subject | Complex Variables | |
| dc.subject | Functional Analysis | |
| dc.subject | 30H05 (Primary); 46E20, 47A15 (Secondary) | |
| dc.title | On the Brown--Shields conjecture for cyclicity in the Dirichlet space | |
| dc.type | text |