JournalsrmiVol. 21, No. 3pp. 911–928

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

  • Manuel D. Contreras

    Universidad de Sevilla, Spain
  • Santiago Díaz-Madrigal

    Universidad de Sevilla, Spain
Fractional iteration in the disk algebra: prime ends and composition operators cover
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Abstract

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 Carath\'eodory about local connection and boundary behaviour of univalent functions.

Cite this article

Manuel D. Contreras, Santiago Díaz-Madrigal, Fractional iteration in the disk algebra: prime ends and composition operators. Rev. Mat. Iberoam. 21 (2005), no. 3, pp. 911–928

DOI 10.4171/RMI/440