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

Manuel D. Contreras; Santiago Díaz-Madrigal

Revista Matemática Iberoamericana (2005)

  • Volume: 21, Issue: 3, page 911-928
  • ISSN: 0213-2230

Abstract

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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.

How to cite

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Contreras, Manuel D., and Díaz-Madrigal, Santiago. "Fractional iteration in the disk algebra: prime ends and composition operators.." Revista Matemática Iberoamericana 21.3 (2005): 911-928. <http://eudml.org/doc/41955>.

@article{Contreras2005,
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 Carathéodory about local connection and boundary behaviour of univalent functions.},
author = {Contreras, Manuel D., Díaz-Madrigal, Santiago},
journal = {Revista Matemática Iberoamericana},
keywords = {Operadores de composición; Algebra del disco; Semigrupo de operadores; semigroups; disk algebra; prime end; starlike functions; spirallike functions},
language = {eng},
number = {3},
pages = {911-928},
title = {Fractional iteration in the disk algebra: prime ends and composition operators.},
url = {http://eudml.org/doc/41955},
volume = {21},
year = {2005},
}

TY - JOUR
AU - Contreras, Manuel D.
AU - Díaz-Madrigal, Santiago
TI - Fractional iteration in the disk algebra: prime ends and composition operators.
JO - Revista Matemática Iberoamericana
PY - 2005
VL - 21
IS - 3
SP - 911
EP - 928
AB - 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.
LA - eng
KW - Operadores de composición; Algebra del disco; Semigrupo de operadores; semigroups; disk algebra; prime end; starlike functions; spirallike functions
UR - http://eudml.org/doc/41955
ER -

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