Mathematics – Functional Analysis
Scientific paper
2005-04-08
Mathematics
Functional Analysis
8 pages, 1 figure. See also http://webdelprofesor.ula.ve/nucleotachira/gchacon or http://webdelprofesor.ula.ve/humanidades/g
Scientific paper
In this paper we investigate the following problem: when a bounded analytic function $\phi$ on the unit disk $\mathbb{D}$, fixing 0, is such that $\{\phi^n : n = 0, 1, 2, . . . \}$ 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 $H^2$.
Chacon Gerardo A.
Chacon Gerardo R.
Gimenez Jose
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