Composition Operators on the Dirichlet Space and Related Problems
| dc.creator | Chacon, Gerardo A. | |
| dc.creator | Chacon, Gerardo R. | |
| dc.creator | Gimenez, Jose | |
| dc.date | 2005-04-08 | |
| dc.date.accessioned | 2026-07-07T05:18:56Z | |
| dc.date.available | 2026-07-07T05:18:56Z | |
| dc.description | In this paper we investigate the following problem: when a bounded analytic function $ϕ$ on the unit disk $\mathbb{D}$, fixing 0, is such that $\{ϕ^n : n = 0, 1, 2, . . . \}$ is orthogonal in $\mathbb{D}$?, and consider the problem of characterizing the univalent, full self-maps of $\mathbb{D}$ in terms of the norm of the composition operator induced. The first problem is analogous to a celebrated question asked by W. Rudin on the Hardy space setting that was answered recently ([3] and [15]). The second problem is analogous to a problem investigated by J. Shapiro in [14] about characterization of inner functions in the setting of $H^2$. | |
| dc.description | 8 pages, 1 figure. See also http://webdelprofesor.ula.ve/nucleotachira/gchacon or http://webdelprofesor.ula.ve/humanidades/grchacon | |
| dc.identifier | https://arxiv.org/abs/math/0504179 | |
| dc.identifier | http://arxiv.org/abs/math/0504179 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74839 | |
| dc.subject | Functional Analysis | |
| dc.subject | Complex Variables | |
| dc.subject | 47B33 (primary); 47B38, 47A16 (secondary) | |
| dc.title | Composition Operators on the Dirichlet Space and Related Problems | |
| dc.type | text |