Displaying similar documents to “Backward-iteration sequences with bounded hyperbolic steps for analytic self-maps of the disk.”

Fractional iteration in the disk algebra: prime ends and composition operators.

Manuel D. Contreras, Santiago Díaz-Madrigal (2005)

Revista Matemática Iberoamericana

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In this paper we characterize the semigroups of analytic functions in the unit disk which lead to semigroups of operators in the disk algebra. These characterizations involve analytic as well as geometric aspects of the iterates and they are strongly related to the classical theorem of Carathéodory about local connection and boundary behaviour of univalent functions.

Completeness in L(R) of discrete translates.

Joaquim Bruna, Alexander Olevskii, Alexander Ulanovskii (2006)

Revista Matemática Iberoamericana

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We characterize, in terms of the Beurling-Malliavin density, the discrete spectra Λ ⊂ R for which a generator exists, that is a function φ ∈ L(R) such that its Λ translates φ(x - λ), λ ∈ Λ, span L(R). It is shown that these spectra coincide with the uniqueness sets for certain analytic clases. We also present examples of discrete spectra Λ ∈ R which do not admit a single generator while they admit a pair of generators.