Reproducing kernels, de Branges-Rovnyak spaces, and norms of weighted composition operators
| dc.creator | Jury, Michael T. | |
| dc.date | 2007-07-23 | |
| dc.date.accessioned | 2026-07-07T08:19:43Z | |
| dc.date.available | 2026-07-07T08:19:43Z | |
| dc.description | We prove that the norm of a weighted composition operator on the Hardy space H^2 of the disk is controlled by the norm of the weight function in the de Branges-Rovnyak space associated to the symbol of the composition operator. As a corollary we obtain a new proof of the boundedness of composition operators on H^2, and recover the standard upper bound for the norm. Similar arguments apply to weighted Bergman spaces. We also show that the positivity of a generalized de Branges-Rovnyak kernel is sufficient for the boundedness of a given composition operator on the standard functions spaces on the unit ball. | |
| dc.description | 9 pages, to appear in Proc. Amer. Math Soc | |
| dc.identifier | https://arxiv.org/abs/0707.3426 | |
| dc.identifier | http://arxiv.org/abs/0707.3426 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/134862 | |
| dc.subject | Functional Analysis | |
| dc.subject | 47B33 (primary), 47B32, 46E22 (secondary) | |
| dc.title | Reproducing kernels, de Branges-Rovnyak spaces, and norms of weighted composition operators | |
| dc.type | text |