RESUMEN

In this paper we investigate the following question: when a bounded analytic function ' on the unit disk D, fixing 0, is such that the family {'n : n = 0, 1, 2, . . . } is orthogonal in the Dirichlet space D?. We also consider the problem of characterizing the univalent, full self-maps ' of D in terms of the norm of the induced composition operator C' : D → D. The first problem is analogous to a celebrated question asked byW. Rudin on the Hardy space setting that was answered recently ([3] and [14]). The second problem resembles a problem investigated by J. Shapiro in [13] about characterization of inner functions _ in the terms of kC_kH2 .

RESUMEN

En este artículo, cuyo carácter es divulgativo, estudiamos algunas propiedades Dinámicas de operadores de composición, con símbolo fraccional lineal, que actúan en espacios de Hilbert Funcionales Analíticos. Asimismo, estudiamos la dinámica de semigrupos de operadores de composición en dichos espacios.