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.
Publié le : 2005-03-14
Classification:
semigroups,
disk algebra,
prime end,
starlike functions,
spirallike functions,
30C45,
30D40,
30H05,
47B33,
47D06,
54D05
@article{1136999136,
author = {Contreras, Manuel D. and D\'\i az-Madrigal, Santiago},
title = {Fractional iteration in the disk algebra: prime ends and composition
operators},
journal = {Rev. Mat. Iberoamericana},
volume = {21},
number = {2},
year = {2005},
pages = { 911-928},
language = {en},
url = {http://dml.mathdoc.fr/item/1136999136}
}
Contreras, Manuel D.; Díaz-Madrigal, Santiago. Fractional iteration in the disk algebra: prime ends and composition
operators. Rev. Mat. Iberoamericana, Tome 21 (2005) no. 2, pp. 911-928. http://gdmltest.u-ga.fr/item/1136999136/