Open Access
December, 2005 Fractional iteration in the disk algebra: prime ends and composition operators
Manuel D. Contreras, Santiago Díaz-Madrigal
Rev. Mat. Iberoamericana 21(3): 911-928 (December, 2005).


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.


Download Citation

Manuel D. Contreras. Santiago Díaz-Madrigal. "Fractional iteration in the disk algebra: prime ends and composition operators." Rev. Mat. Iberoamericana 21 (3) 911 - 928, December, 2005.


Published: December, 2005
First available in Project Euclid: 11 January 2006

zbMATH: 1103.30034
MathSciNet: MR2231015

Primary: 30C45 , 30D40 , ‎30H05 , 47B33 , 47D06
Secondary: 54D05

Keywords: disk algebra , prime end , semigroups , spirallike functions , Starlike functions

Rights: Copyright © 2005 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.21 • No. 3 • December, 2005
Back to Top