Equivalence of summatory conditions along sequences for bounded holomorphic functions
| dc.creator | Eiderman, Vladimir Ya. | |
| dc.creator | Thomas, Pascal J. | |
| dc.date | 2003-06-26 | |
| dc.date | 2003-11-24 | |
| dc.date.accessioned | 2026-07-07T04:59:12Z | |
| dc.date.available | 2026-07-07T04:59:12Z | |
| dc.description | A sequence of points $z_k$ in the unit disk is said to be thin for a given decrease function $ρ$, if there is a nontrivial bounded holomorphic function such that the infinite series $\sum_k ρ(1-|z_k|)|f(z_k)|$ converges. All sequences will be assumed hyperbolically separated. We give necessary and sufficient conditions for the problem of thinness of a sequence to be non-trivial (one way or the other), and for two different decrease functions to give rise to the same thin sequences. Along the way, some concrete conditions (necessary or sufficient) for a sequence to be thin are obtained. | |
| dc.description | 15 pages, LaTeX; some typos corrected. To appear in the issue of Complex Variables dedicated to the memory of Matts Essen | |
| dc.identifier | https://arxiv.org/abs/math/0306376 | |
| dc.identifier | http://arxiv.org/abs/math/0306376 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67890 | |
| dc.subject | Complex Variables | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 30D50 | |
| dc.title | Equivalence of summatory conditions along sequences for bounded holomorphic functions | |
| dc.type | text |