Integral representation of the $n$-th derivative in de Branges-Rovnyak spaces and the norm convergence of its reproducing kernel
| dc.creator | Fricain, Emmanuel | |
| dc.creator | Mashreghi, Javad | |
| dc.date | 2008-02-06 | |
| dc.date.accessioned | 2026-07-07T09:19:02Z | |
| dc.date.available | 2026-07-07T09:19:02Z | |
| dc.description | In this paper, we give an integral representation for the boundary values of derivatives of functions of the de Branges--Rovnyak spaces $\HH(b)$, where $b$ is in the unit ball of $H^\infty(\CC_+)$. In particular, we generalize a result of Ahern--Clark obtained for functions of the model spaces $K_b$, where $b$ is an inner function. Using hypergeometric series, we obtain a nontrivial formula of combinatorics for sums of binomial coefficients. Then we apply this formula to show the norm convergence of reproducing kernel $k_{ω,n}^b$ of the evaluation of $n$-th derivative of elements of $\HH(b)$ at the point $ω$ as it tends radially to a point of the real axis. | |
| dc.identifier | https://arxiv.org/abs/0802.0792 | |
| dc.identifier | http://arxiv.org/abs/0802.0792 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/154242 | |
| dc.subject | Complex Variables | |
| dc.subject | Combinatorics | |
| dc.subject | Functional Analysis | |
| dc.title | Integral representation of the $n$-th derivative in de Branges-Rovnyak spaces and the norm convergence of its reproducing kernel | |
| dc.type | text |